Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators
Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and suff...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ay, Serdar [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer International Publishing 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Integral equations and operator theory - Berlin : Springer, 1978, 87(2017), 2 vom: Feb., Seite 263-307 |
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| Übergeordnetes Werk: |
volume:87 ; year:2017 ; number:2 ; month:02 ; pages:263-307 |
| Links: |
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| DOI / URN: |
10.1007/s00020-017-2346-1 |
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| Katalog-ID: |
SPR000194948 |
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| 245 | 1 | 0 | |a Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators |
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| 520 | |a Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. | ||
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| 650 | 4 | |a -space |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Admissible space |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a VH-space |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Positive semidefinite kernel |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -semigroup |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Invariant kernel |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Linearisation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Reproducing kernel |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -representation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Locally |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -algebra |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Hilbert locally |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -module |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Completely positive map |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Gheondea, Aurelian |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Integral equations and operator theory |d Berlin : Springer, 1978 |g 87(2017), 2 vom: Feb., Seite 263-307 |w (DE-627)365149993 |w (DE-600)2111640-4 |x 1420-8989 |7 nnns |
| 773 | 1 | 8 | |g volume:87 |g year:2017 |g number:2 |g month:02 |g pages:263-307 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00020-017-2346-1 |z lizenzpflichtig |3 Volltext |
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10.1007/s00020-017-2346-1 doi (DE-627)SPR000194948 (SPR)s00020-017-2346-1-e DE-627 ger DE-627 rakwb eng Ay, Serdar verfasserin aut Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. Ordered (dpeaa)DE-He213 -space (dpeaa)DE-He213 Admissible space (dpeaa)DE-He213 VH-space (dpeaa)DE-He213 Positive semidefinite kernel (dpeaa)DE-He213 -semigroup (dpeaa)DE-He213 Invariant kernel (dpeaa)DE-He213 Linearisation (dpeaa)DE-He213 Reproducing kernel (dpeaa)DE-He213 -representation (dpeaa)DE-He213 Locally (dpeaa)DE-He213 -algebra (dpeaa)DE-He213 Hilbert locally (dpeaa)DE-He213 -module (dpeaa)DE-He213 Completely positive map (dpeaa)DE-He213 Gheondea, Aurelian aut Enthalten in Integral equations and operator theory Berlin : Springer, 1978 87(2017), 2 vom: Feb., Seite 263-307 (DE-627)365149993 (DE-600)2111640-4 1420-8989 nnns volume:87 year:2017 number:2 month:02 pages:263-307 https://dx.doi.org/10.1007/s00020-017-2346-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 87 2017 2 02 263-307 |
| spelling |
10.1007/s00020-017-2346-1 doi (DE-627)SPR000194948 (SPR)s00020-017-2346-1-e DE-627 ger DE-627 rakwb eng Ay, Serdar verfasserin aut Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. Ordered (dpeaa)DE-He213 -space (dpeaa)DE-He213 Admissible space (dpeaa)DE-He213 VH-space (dpeaa)DE-He213 Positive semidefinite kernel (dpeaa)DE-He213 -semigroup (dpeaa)DE-He213 Invariant kernel (dpeaa)DE-He213 Linearisation (dpeaa)DE-He213 Reproducing kernel (dpeaa)DE-He213 -representation (dpeaa)DE-He213 Locally (dpeaa)DE-He213 -algebra (dpeaa)DE-He213 Hilbert locally (dpeaa)DE-He213 -module (dpeaa)DE-He213 Completely positive map (dpeaa)DE-He213 Gheondea, Aurelian aut Enthalten in Integral equations and operator theory Berlin : Springer, 1978 87(2017), 2 vom: Feb., Seite 263-307 (DE-627)365149993 (DE-600)2111640-4 1420-8989 nnns volume:87 year:2017 number:2 month:02 pages:263-307 https://dx.doi.org/10.1007/s00020-017-2346-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 87 2017 2 02 263-307 |
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10.1007/s00020-017-2346-1 doi (DE-627)SPR000194948 (SPR)s00020-017-2346-1-e DE-627 ger DE-627 rakwb eng Ay, Serdar verfasserin aut Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. Ordered (dpeaa)DE-He213 -space (dpeaa)DE-He213 Admissible space (dpeaa)DE-He213 VH-space (dpeaa)DE-He213 Positive semidefinite kernel (dpeaa)DE-He213 -semigroup (dpeaa)DE-He213 Invariant kernel (dpeaa)DE-He213 Linearisation (dpeaa)DE-He213 Reproducing kernel (dpeaa)DE-He213 -representation (dpeaa)DE-He213 Locally (dpeaa)DE-He213 -algebra (dpeaa)DE-He213 Hilbert locally (dpeaa)DE-He213 -module (dpeaa)DE-He213 Completely positive map (dpeaa)DE-He213 Gheondea, Aurelian aut Enthalten in Integral equations and operator theory Berlin : Springer, 1978 87(2017), 2 vom: Feb., Seite 263-307 (DE-627)365149993 (DE-600)2111640-4 1420-8989 nnns volume:87 year:2017 number:2 month:02 pages:263-307 https://dx.doi.org/10.1007/s00020-017-2346-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 87 2017 2 02 263-307 |
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10.1007/s00020-017-2346-1 doi (DE-627)SPR000194948 (SPR)s00020-017-2346-1-e DE-627 ger DE-627 rakwb eng Ay, Serdar verfasserin aut Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. Ordered (dpeaa)DE-He213 -space (dpeaa)DE-He213 Admissible space (dpeaa)DE-He213 VH-space (dpeaa)DE-He213 Positive semidefinite kernel (dpeaa)DE-He213 -semigroup (dpeaa)DE-He213 Invariant kernel (dpeaa)DE-He213 Linearisation (dpeaa)DE-He213 Reproducing kernel (dpeaa)DE-He213 -representation (dpeaa)DE-He213 Locally (dpeaa)DE-He213 -algebra (dpeaa)DE-He213 Hilbert locally (dpeaa)DE-He213 -module (dpeaa)DE-He213 Completely positive map (dpeaa)DE-He213 Gheondea, Aurelian aut Enthalten in Integral equations and operator theory Berlin : Springer, 1978 87(2017), 2 vom: Feb., Seite 263-307 (DE-627)365149993 (DE-600)2111640-4 1420-8989 nnns volume:87 year:2017 number:2 month:02 pages:263-307 https://dx.doi.org/10.1007/s00020-017-2346-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 87 2017 2 02 263-307 |
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10.1007/s00020-017-2346-1 doi (DE-627)SPR000194948 (SPR)s00020-017-2346-1-e DE-627 ger DE-627 rakwb eng Ay, Serdar verfasserin aut Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. Ordered (dpeaa)DE-He213 -space (dpeaa)DE-He213 Admissible space (dpeaa)DE-He213 VH-space (dpeaa)DE-He213 Positive semidefinite kernel (dpeaa)DE-He213 -semigroup (dpeaa)DE-He213 Invariant kernel (dpeaa)DE-He213 Linearisation (dpeaa)DE-He213 Reproducing kernel (dpeaa)DE-He213 -representation (dpeaa)DE-He213 Locally (dpeaa)DE-He213 -algebra (dpeaa)DE-He213 Hilbert locally (dpeaa)DE-He213 -module (dpeaa)DE-He213 Completely positive map (dpeaa)DE-He213 Gheondea, Aurelian aut Enthalten in Integral equations and operator theory Berlin : Springer, 1978 87(2017), 2 vom: Feb., Seite 263-307 (DE-627)365149993 (DE-600)2111640-4 1420-8989 nnns volume:87 year:2017 number:2 month:02 pages:263-307 https://dx.doi.org/10.1007/s00020-017-2346-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 87 2017 2 02 263-307 |
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Enthalten in Integral equations and operator theory 87(2017), 2 vom: Feb., Seite 263-307 volume:87 year:2017 number:2 month:02 pages:263-307 |
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Enthalten in Integral equations and operator theory 87(2017), 2 vom: Feb., Seite 263-307 volume:87 year:2017 number:2 month:02 pages:263-307 |
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Ordered -space Admissible space VH-space Positive semidefinite kernel -semigroup Invariant kernel Linearisation Reproducing kernel -representation Locally -algebra Hilbert locally -module Completely positive map |
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Ay, Serdar @@aut@@ Gheondea, Aurelian @@aut@@ |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR000194948</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327141753.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2017 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00020-017-2346-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR000194948</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00020-017-2346-1-e</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="100" ind1="1" ind2=" "><subfield code="a">Ay, Serdar</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer International Publishing 2017</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ordered</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-space</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Admissible space</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">VH-space</subfield><subfield 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Ay, Serdar |
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Ay, Serdar misc Ordered misc -space misc Admissible space misc VH-space misc Positive semidefinite kernel misc -semigroup misc Invariant kernel misc Linearisation misc Reproducing kernel misc -representation misc Locally misc -algebra misc Hilbert locally misc -module misc Completely positive map Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators |
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Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators Ordered (dpeaa)DE-He213 -space (dpeaa)DE-He213 Admissible space (dpeaa)DE-He213 VH-space (dpeaa)DE-He213 Positive semidefinite kernel (dpeaa)DE-He213 -semigroup (dpeaa)DE-He213 Invariant kernel (dpeaa)DE-He213 Linearisation (dpeaa)DE-He213 Reproducing kernel (dpeaa)DE-He213 -representation (dpeaa)DE-He213 Locally (dpeaa)DE-He213 -algebra (dpeaa)DE-He213 Hilbert locally (dpeaa)DE-He213 -module (dpeaa)DE-He213 Completely positive map (dpeaa)DE-He213 |
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misc Ordered misc -space misc Admissible space misc VH-space misc Positive semidefinite kernel misc -semigroup misc Invariant kernel misc Linearisation misc Reproducing kernel misc -representation misc Locally misc -algebra misc Hilbert locally misc -module misc Completely positive map |
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misc Ordered misc -space misc Admissible space misc VH-space misc Positive semidefinite kernel misc -semigroup misc Invariant kernel misc Linearisation misc Reproducing kernel misc -representation misc Locally misc -algebra misc Hilbert locally misc -module misc Completely positive map |
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misc Ordered misc -space misc Admissible space misc VH-space misc Positive semidefinite kernel misc -semigroup misc Invariant kernel misc Linearisation misc Reproducing kernel misc -representation misc Locally misc -algebra misc Hilbert locally misc -module misc Completely positive map |
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Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators |
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Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators |
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Integral equations and operator theory |
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Ay, Serdar Gheondea, Aurelian |
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representations of %$\varvec{*}%$-semigroups associated to invariant kernels with values continuously adjointable operators |
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Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators |
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Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. © Springer International Publishing 2017 |
| abstractGer |
Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. © Springer International Publishing 2017 |
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Abstract We consider positive semidefinite kernels valued in the %$*%$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of %$*%$-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist %$*%$-representations of the underlying %$*%$-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled. For example, when specialising to the case of Hilbert modules over locally %$C^*%$-algebras, we show that both boundedness conditions are automatically fulfilled and, consequently, this general approach provides a rather direct proof of the general Stinespring–Kasparov type dilation theorem for completely positive maps on locally %$C^*%$-algebras and with values adjointable operators on Hilbert modules over locally %$C^*%$-algebras. © Springer International Publishing 2017 |
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Representations of %$\varvec{*}%$-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators |
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| score |
7.400985 |