Between the von Neumann inequality and the Crouzeix conjecture
A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincid...
Ausführliche Beschreibung
Gespeichert in:
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Pagacz, Patryk [verfasserIn] |
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Englisch |
| Erschienen: |
2020 |
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| Umfang: |
28 |
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| Übergeordnetes Werk: |
Enthalten in: CFD investigation on particle deposition in aligned and staggered ribbed duct air flows - Lu, Hao ELSEVIER, 2016, LAA, New York, NY |
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| Übergeordnetes Werk: |
volume:605 ; year:2020 ; day:15 ; month:11 ; pages:130-157 ; extent:28 |
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10.1016/j.laa.2020.07.002 |
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| 520 | |a A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincides with the numerical range. It is also shown that W ρ ( T ) is contained in the closed unit disc if and only if T has a ρ unitary dilation in the sense of Nágy-Foiaş. The spectral constant of W ρ ( T ) is investigated, it is shown that it is monotone and continuous with respect to the parameter ρ. | ||
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10.1016/j.laa.2020.07.002 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001116.pica (DE-627)ELV051199998 (ELSEVIER)S0024-3795(20)30325-6 DE-627 ger DE-627 rakwb eng 690 VZ 530 620 VZ 52.56 bkl Pagacz, Patryk verfasserin aut Between the von Neumann inequality and the Crouzeix conjecture 2020 28 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincides with the numerical range. It is also shown that W ρ ( T ) is contained in the closed unit disc if and only if T has a ρ unitary dilation in the sense of Nágy-Foiaş. The spectral constant of W ρ ( T ) is investigated, it is shown that it is monotone and continuous with respect to the parameter ρ. secondary Elsevier 47A25 Elsevier 47A56 Elsevier 47A20 Elsevier 47A63 Elsevier primary Elsevier Pietrzycki, Paweł oth Wojtylak, Michał oth Enthalten in American Elsevier Publ Lu, Hao ELSEVIER CFD investigation on particle deposition in aligned and staggered ribbed duct air flows 2016 LAA New York, NY (DE-627)ELV014483130 volume:605 year:2020 day:15 month:11 pages:130-157 extent:28 https://doi.org/10.1016/j.laa.2020.07.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 GBV_ILN_2015 GBV_ILN_2021 52.56 Regenerative Energieformen alternative Energieformen VZ AR 605 2020 15 1115 130-157 28 |
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10.1016/j.laa.2020.07.002 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001116.pica (DE-627)ELV051199998 (ELSEVIER)S0024-3795(20)30325-6 DE-627 ger DE-627 rakwb eng 690 VZ 530 620 VZ 52.56 bkl Pagacz, Patryk verfasserin aut Between the von Neumann inequality and the Crouzeix conjecture 2020 28 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincides with the numerical range. It is also shown that W ρ ( T ) is contained in the closed unit disc if and only if T has a ρ unitary dilation in the sense of Nágy-Foiaş. The spectral constant of W ρ ( T ) is investigated, it is shown that it is monotone and continuous with respect to the parameter ρ. secondary Elsevier 47A25 Elsevier 47A56 Elsevier 47A20 Elsevier 47A63 Elsevier primary Elsevier Pietrzycki, Paweł oth Wojtylak, Michał oth Enthalten in American Elsevier Publ Lu, Hao ELSEVIER CFD investigation on particle deposition in aligned and staggered ribbed duct air flows 2016 LAA New York, NY (DE-627)ELV014483130 volume:605 year:2020 day:15 month:11 pages:130-157 extent:28 https://doi.org/10.1016/j.laa.2020.07.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 GBV_ILN_2015 GBV_ILN_2021 52.56 Regenerative Energieformen alternative Energieformen VZ AR 605 2020 15 1115 130-157 28 |
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10.1016/j.laa.2020.07.002 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001116.pica (DE-627)ELV051199998 (ELSEVIER)S0024-3795(20)30325-6 DE-627 ger DE-627 rakwb eng 690 VZ 530 620 VZ 52.56 bkl Pagacz, Patryk verfasserin aut Between the von Neumann inequality and the Crouzeix conjecture 2020 28 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincides with the numerical range. It is also shown that W ρ ( T ) is contained in the closed unit disc if and only if T has a ρ unitary dilation in the sense of Nágy-Foiaş. The spectral constant of W ρ ( T ) is investigated, it is shown that it is monotone and continuous with respect to the parameter ρ. secondary Elsevier 47A25 Elsevier 47A56 Elsevier 47A20 Elsevier 47A63 Elsevier primary Elsevier Pietrzycki, Paweł oth Wojtylak, Michał oth Enthalten in American Elsevier Publ Lu, Hao ELSEVIER CFD investigation on particle deposition in aligned and staggered ribbed duct air flows 2016 LAA New York, NY (DE-627)ELV014483130 volume:605 year:2020 day:15 month:11 pages:130-157 extent:28 https://doi.org/10.1016/j.laa.2020.07.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 GBV_ILN_2015 GBV_ILN_2021 52.56 Regenerative Energieformen alternative Energieformen VZ AR 605 2020 15 1115 130-157 28 |
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10.1016/j.laa.2020.07.002 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001116.pica (DE-627)ELV051199998 (ELSEVIER)S0024-3795(20)30325-6 DE-627 ger DE-627 rakwb eng 690 VZ 530 620 VZ 52.56 bkl Pagacz, Patryk verfasserin aut Between the von Neumann inequality and the Crouzeix conjecture 2020 28 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincides with the numerical range. It is also shown that W ρ ( T ) is contained in the closed unit disc if and only if T has a ρ unitary dilation in the sense of Nágy-Foiaş. The spectral constant of W ρ ( T ) is investigated, it is shown that it is monotone and continuous with respect to the parameter ρ. secondary Elsevier 47A25 Elsevier 47A56 Elsevier 47A20 Elsevier 47A63 Elsevier primary Elsevier Pietrzycki, Paweł oth Wojtylak, Michał oth Enthalten in American Elsevier Publ Lu, Hao ELSEVIER CFD investigation on particle deposition in aligned and staggered ribbed duct air flows 2016 LAA New York, NY (DE-627)ELV014483130 volume:605 year:2020 day:15 month:11 pages:130-157 extent:28 https://doi.org/10.1016/j.laa.2020.07.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 GBV_ILN_2015 GBV_ILN_2021 52.56 Regenerative Energieformen alternative Energieformen VZ AR 605 2020 15 1115 130-157 28 |
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A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincides with the numerical range. It is also shown that W ρ ( T ) is contained in the closed unit disc if and only if T has a ρ unitary dilation in the sense of Nágy-Foiaş. The spectral constant of W ρ ( T ) is investigated, it is shown that it is monotone and continuous with respect to the parameter ρ. |
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A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincides with the numerical range. It is also shown that W ρ ( T ) is contained in the closed unit disc if and only if T has a ρ unitary dilation in the sense of Nágy-Foiaş. The spectral constant of W ρ ( T ) is investigated, it is shown that it is monotone and continuous with respect to the parameter ρ. |
| abstract_unstemmed |
A new concept of a deformed numerical range W ρ ( T ) is introduced. Here T is a bounded linear operator or a matrix and ρ ∈ [ 1 , + ∞ ) is a parameter. Each W ρ ( T ) is a closed convex set that contains the spectrum of T. Furthermore, W ρ ( T ) is decreasing with respect to ρ and W 2 ( T ) coincides with the numerical range. It is also shown that W ρ ( T ) is contained in the closed unit disc if and only if T has a ρ unitary dilation in the sense of Nágy-Foiaş. The spectral constant of W ρ ( T ) is investigated, it is shown that it is monotone and continuous with respect to the parameter ρ. |
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| title_short |
Between the von Neumann inequality and the Crouzeix conjecture |
| url |
https://doi.org/10.1016/j.laa.2020.07.002 |
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| author2 |
Pietrzycki, Paweł Wojtylak, Michał |
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Pietrzycki, Paweł Wojtylak, Michał |
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| doi_str |
10.1016/j.laa.2020.07.002 |
| up_date |
2024-07-06T19:36:08.851Z |
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