The failure of rational dilation on the tetrablock
We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for whic...
Ausführliche Beschreibung
Autor*in: |
Pal, Sourav [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2015transfer abstract |
---|
Schlagwörter: |
---|
Umfang: |
22 |
---|
Übergeordnetes Werk: |
Enthalten in: Corrigendum to “Rifampicin resistance mutations in the rpoB gene of - Urusova, Darya V. ELSEVIER, 2022, Amsterdam [u.a.] |
---|---|
Übergeordnetes Werk: |
volume:269 ; year:2015 ; number:7 ; day:1 ; month:10 ; pages:1903-1924 ; extent:22 |
Links: |
---|
DOI / URN: |
10.1016/j.jfa.2015.07.006 |
---|
Katalog-ID: |
ELV024005509 |
---|
LEADER | 01000caa a22002652 4500 | ||
---|---|---|---|
001 | ELV024005509 | ||
003 | DE-627 | ||
005 | 20230625142021.0 | ||
007 | cr uuu---uuuuu | ||
008 | 180603s2015 xx |||||o 00| ||eng c | ||
024 | 7 | |a 10.1016/j.jfa.2015.07.006 |2 doi | |
028 | 5 | 2 | |a GBVA2015022000016.pica |
035 | |a (DE-627)ELV024005509 | ||
035 | |a (ELSEVIER)S0022-1236(15)00284-0 | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng | ||
082 | 0 | |a 510 | |
082 | 0 | 4 | |a 510 |q DE-600 |
082 | 0 | 4 | |a 570 |q VZ |
084 | |a BIODIV |q DE-30 |2 fid | ||
084 | |a 44.00 |2 bkl | ||
100 | 1 | |a Pal, Sourav |e verfasserin |4 aut | |
245 | 1 | 4 | |a The failure of rational dilation on the tetrablock |
264 | 1 | |c 2015transfer abstract | |
300 | |a 22 | ||
336 | |a nicht spezifiziert |b zzz |2 rdacontent | ||
337 | |a nicht spezifiziert |b z |2 rdamedia | ||
338 | |a nicht spezifiziert |b zu |2 rdacarrier | ||
520 | |a We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. | ||
520 | |a We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. | ||
650 | 7 | |a 47A15 |2 Elsevier | |
650 | 7 | |a 47A13 |2 Elsevier | |
650 | 7 | |a 47A25 |2 Elsevier | |
650 | 7 | |a 47A45 |2 Elsevier | |
650 | 7 | |a 47A20 |2 Elsevier | |
773 | 0 | 8 | |i Enthalten in |n Elsevier |a Urusova, Darya V. ELSEVIER |t Corrigendum to “Rifampicin resistance mutations in the rpoB gene of |d 2022 |g Amsterdam [u.a.] |w (DE-627)ELV007566018 |
773 | 1 | 8 | |g volume:269 |g year:2015 |g number:7 |g day:1 |g month:10 |g pages:1903-1924 |g extent:22 |
856 | 4 | 0 | |u https://doi.org/10.1016/j.jfa.2015.07.006 |3 Volltext |
912 | |a GBV_USEFLAG_U | ||
912 | |a GBV_ELV | ||
912 | |a SYSFLAG_U | ||
912 | |a FID-BIODIV | ||
912 | |a SSG-OLC-PHA | ||
936 | b | k | |a 44.00 |j Medizin: Allgemeines |q VZ |
951 | |a AR | ||
952 | |d 269 |j 2015 |e 7 |b 1 |c 1001 |h 1903-1924 |g 22 | ||
953 | |2 045F |a 510 |
author_variant |
s p sp |
---|---|
matchkey_str |
palsourav:2015----:hfiuefainliainn |
hierarchy_sort_str |
2015transfer abstract |
bklnumber |
44.00 |
publishDate |
2015 |
allfields |
10.1016/j.jfa.2015.07.006 doi GBVA2015022000016.pica (DE-627)ELV024005509 (ELSEVIER)S0022-1236(15)00284-0 DE-627 ger DE-627 rakwb eng 510 510 DE-600 570 VZ BIODIV DE-30 fid 44.00 bkl Pal, Sourav verfasserin aut The failure of rational dilation on the tetrablock 2015transfer abstract 22 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 Elsevier Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:269 year:2015 number:7 day:1 month:10 pages:1903-1924 extent:22 https://doi.org/10.1016/j.jfa.2015.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 269 2015 7 1 1001 1903-1924 22 045F 510 |
spelling |
10.1016/j.jfa.2015.07.006 doi GBVA2015022000016.pica (DE-627)ELV024005509 (ELSEVIER)S0022-1236(15)00284-0 DE-627 ger DE-627 rakwb eng 510 510 DE-600 570 VZ BIODIV DE-30 fid 44.00 bkl Pal, Sourav verfasserin aut The failure of rational dilation on the tetrablock 2015transfer abstract 22 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 Elsevier Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:269 year:2015 number:7 day:1 month:10 pages:1903-1924 extent:22 https://doi.org/10.1016/j.jfa.2015.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 269 2015 7 1 1001 1903-1924 22 045F 510 |
allfields_unstemmed |
10.1016/j.jfa.2015.07.006 doi GBVA2015022000016.pica (DE-627)ELV024005509 (ELSEVIER)S0022-1236(15)00284-0 DE-627 ger DE-627 rakwb eng 510 510 DE-600 570 VZ BIODIV DE-30 fid 44.00 bkl Pal, Sourav verfasserin aut The failure of rational dilation on the tetrablock 2015transfer abstract 22 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 Elsevier Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:269 year:2015 number:7 day:1 month:10 pages:1903-1924 extent:22 https://doi.org/10.1016/j.jfa.2015.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 269 2015 7 1 1001 1903-1924 22 045F 510 |
allfieldsGer |
10.1016/j.jfa.2015.07.006 doi GBVA2015022000016.pica (DE-627)ELV024005509 (ELSEVIER)S0022-1236(15)00284-0 DE-627 ger DE-627 rakwb eng 510 510 DE-600 570 VZ BIODIV DE-30 fid 44.00 bkl Pal, Sourav verfasserin aut The failure of rational dilation on the tetrablock 2015transfer abstract 22 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 Elsevier Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:269 year:2015 number:7 day:1 month:10 pages:1903-1924 extent:22 https://doi.org/10.1016/j.jfa.2015.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 269 2015 7 1 1001 1903-1924 22 045F 510 |
allfieldsSound |
10.1016/j.jfa.2015.07.006 doi GBVA2015022000016.pica (DE-627)ELV024005509 (ELSEVIER)S0022-1236(15)00284-0 DE-627 ger DE-627 rakwb eng 510 510 DE-600 570 VZ BIODIV DE-30 fid 44.00 bkl Pal, Sourav verfasserin aut The failure of rational dilation on the tetrablock 2015transfer abstract 22 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 Elsevier Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:269 year:2015 number:7 day:1 month:10 pages:1903-1924 extent:22 https://doi.org/10.1016/j.jfa.2015.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 269 2015 7 1 1001 1903-1924 22 045F 510 |
language |
English |
source |
Enthalten in Corrigendum to “Rifampicin resistance mutations in the rpoB gene of Amsterdam [u.a.] volume:269 year:2015 number:7 day:1 month:10 pages:1903-1924 extent:22 |
sourceStr |
Enthalten in Corrigendum to “Rifampicin resistance mutations in the rpoB gene of Amsterdam [u.a.] volume:269 year:2015 number:7 day:1 month:10 pages:1903-1924 extent:22 |
format_phy_str_mv |
Article |
bklname |
Medizin: Allgemeines |
institution |
findex.gbv.de |
topic_facet |
47A15 47A13 47A25 47A45 47A20 |
dewey-raw |
510 |
isfreeaccess_bool |
false |
container_title |
Corrigendum to “Rifampicin resistance mutations in the rpoB gene of |
authorswithroles_txt_mv |
Pal, Sourav @@aut@@ |
publishDateDaySort_date |
2015-01-01T00:00:00Z |
hierarchy_top_id |
ELV007566018 |
dewey-sort |
3510 |
id |
ELV024005509 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV024005509</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625142021.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.jfa.2015.07.006</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2015022000016.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV024005509</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0022-1236(15)00284-0</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">570</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">BIODIV</subfield><subfield code="q">DE-30</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pal, Sourav</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The failure of rational dilation on the tetrablock</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">22</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A15</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A13</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A25</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A45</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A20</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier</subfield><subfield code="a">Urusova, Darya V. ELSEVIER</subfield><subfield code="t">Corrigendum to “Rifampicin resistance mutations in the rpoB gene of</subfield><subfield code="d">2022</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV007566018</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:269</subfield><subfield code="g">year:2015</subfield><subfield code="g">number:7</subfield><subfield code="g">day:1</subfield><subfield code="g">month:10</subfield><subfield code="g">pages:1903-1924</subfield><subfield code="g">extent:22</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.jfa.2015.07.006</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-BIODIV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.00</subfield><subfield code="j">Medizin: Allgemeines</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">269</subfield><subfield code="j">2015</subfield><subfield code="e">7</subfield><subfield code="b">1</subfield><subfield code="c">1001</subfield><subfield code="h">1903-1924</subfield><subfield code="g">22</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">510</subfield></datafield></record></collection>
|
author |
Pal, Sourav |
spellingShingle |
Pal, Sourav ddc 510 ddc 570 fid BIODIV bkl 44.00 Elsevier 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 The failure of rational dilation on the tetrablock |
authorStr |
Pal, Sourav |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)ELV007566018 |
format |
electronic Article |
dewey-ones |
510 - Mathematics 570 - Life sciences; biology |
delete_txt_mv |
keep |
author_role |
aut |
collection |
elsevier |
remote_str |
true |
illustrated |
Not Illustrated |
topic_title |
510 510 DE-600 570 VZ BIODIV DE-30 fid 44.00 bkl The failure of rational dilation on the tetrablock 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 Elsevier |
topic |
ddc 510 ddc 570 fid BIODIV bkl 44.00 Elsevier 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 |
topic_unstemmed |
ddc 510 ddc 570 fid BIODIV bkl 44.00 Elsevier 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 |
topic_browse |
ddc 510 ddc 570 fid BIODIV bkl 44.00 Elsevier 47A15 Elsevier 47A13 Elsevier 47A25 Elsevier 47A45 Elsevier 47A20 |
format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
zu |
hierarchy_parent_title |
Corrigendum to “Rifampicin resistance mutations in the rpoB gene of |
hierarchy_parent_id |
ELV007566018 |
dewey-tens |
510 - Mathematics 570 - Life sciences; biology |
hierarchy_top_title |
Corrigendum to “Rifampicin resistance mutations in the rpoB gene of |
isfreeaccess_txt |
false |
familylinks_str_mv |
(DE-627)ELV007566018 |
title |
The failure of rational dilation on the tetrablock |
ctrlnum |
(DE-627)ELV024005509 (ELSEVIER)S0022-1236(15)00284-0 |
title_full |
The failure of rational dilation on the tetrablock |
author_sort |
Pal, Sourav |
journal |
Corrigendum to “Rifampicin resistance mutations in the rpoB gene of |
journalStr |
Corrigendum to “Rifampicin resistance mutations in the rpoB gene of |
lang_code |
eng |
isOA_bool |
false |
dewey-hundreds |
500 - Science |
recordtype |
marc |
publishDateSort |
2015 |
contenttype_str_mv |
zzz |
container_start_page |
1903 |
author_browse |
Pal, Sourav |
container_volume |
269 |
physical |
22 |
class |
510 510 DE-600 570 VZ BIODIV DE-30 fid 44.00 bkl |
format_se |
Elektronische Aufsätze |
author-letter |
Pal, Sourav |
doi_str_mv |
10.1016/j.jfa.2015.07.006 |
dewey-full |
510 570 |
title_sort |
failure of rational dilation on the tetrablock |
title_auth |
The failure of rational dilation on the tetrablock |
abstract |
We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. |
abstractGer |
We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. |
abstract_unstemmed |
We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model. |
collection_details |
GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA |
container_issue |
7 |
title_short |
The failure of rational dilation on the tetrablock |
url |
https://doi.org/10.1016/j.jfa.2015.07.006 |
remote_bool |
true |
ppnlink |
ELV007566018 |
mediatype_str_mv |
z |
isOA_txt |
false |
hochschulschrift_bool |
false |
doi_str |
10.1016/j.jfa.2015.07.006 |
up_date |
2024-07-06T20:17:10.247Z |
_version_ |
1803862178790375424 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV024005509</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625142021.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.jfa.2015.07.006</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2015022000016.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV024005509</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0022-1236(15)00284-0</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">570</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">BIODIV</subfield><subfield code="q">DE-30</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pal, Sourav</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The failure of rational dilation on the tetrablock</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">22</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C 3 defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . A commuting triple of operators ( T 1 , T 2 , T 3 ) for which the closed tetrablock E ‾ is a spectral set, is called an E -contraction. For an E -contraction ( T 1 , T 2 , T 3 ) , the two operator equations T 1 − T 2 ⁎ T 3 = D T 3 X 1 D T 3 and T 2 − T 1 ⁎ T 3 = D T 3 X 2 D T 3 , D T 3 = ( I − T 3 ⁎ T 3 ) 1 2 , have unique solutions A 1 , A 2 on D T 3 = Ran ‾ D T 3 and they are called the fundamental operators of ( T 1 , T 2 , T 3 ) . For a particular class of E -contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators A 1 , A 2 satisfy (0.1) A 1 A 2 = A 2 A 1 and A 1 ⁎ A 1 − A 1 A 1 ⁎ = A 2 ⁎ A 2 − A 2 A 2 ⁎ . Then we construct an E -contraction from that particular class which fails to satisfy (0.1). We produce a concrete functional model for pure E -isometries, a class of E -contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A15</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A13</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A25</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A45</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">47A20</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier</subfield><subfield code="a">Urusova, Darya V. ELSEVIER</subfield><subfield code="t">Corrigendum to “Rifampicin resistance mutations in the rpoB gene of</subfield><subfield code="d">2022</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV007566018</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:269</subfield><subfield code="g">year:2015</subfield><subfield code="g">number:7</subfield><subfield code="g">day:1</subfield><subfield code="g">month:10</subfield><subfield code="g">pages:1903-1924</subfield><subfield code="g">extent:22</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.jfa.2015.07.006</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-BIODIV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.00</subfield><subfield code="j">Medizin: Allgemeines</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">269</subfield><subfield code="j">2015</subfield><subfield code="e">7</subfield><subfield code="b">1</subfield><subfield code="c">1001</subfield><subfield code="h">1903-1924</subfield><subfield code="g">22</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">510</subfield></datafield></record></collection>
|
score |
7.3998823 |