SPECTRAL SETS AND OPERATOR RADII
Document type :
Article dans une revue scientifique: Article original
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Title :
SPECTRAL SETS AND OPERATOR RADII
Author(s) :
Badea, Catalin [Auteur correspondant]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Crouzeix, Michel [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Klaja, Hubert [Auteur]
Centrale Lille

Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Crouzeix, Michel [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Klaja, Hubert [Auteur]
Centrale Lille
Journal title :
Bulletin of the London Mathematical Society
Pages :
986-996
Publisher :
London Mathematical Society
Publication date :
2018
ISSN :
0024-6093
HAL domain(s) :
Mathématiques [math]/Analyse fonctionnelle [math.FA]
English abstract : [en]
We study different operator radii of homomorphisms from an operator algebra into B(H) and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if Ω is a K-spectral set for ...
Show more >We study different operator radii of homomorphisms from an operator algebra into B(H) and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if Ω is a K-spectral set for a Hilbert space operator, then it is a M-numerical radius set, where M = 1/2 (K + K ^{−1}). This is a counterpart of a recent result of Davidson, Paulsen and Woerdeman. More general results for operator radii associated with the class of operators having ρ-dilations in the sense of Sz.-Nagy and Foias are given. A version of a result of Drury concerning the joint numerical radius of non-commuting n-tuples of operators is also obtained.Show less >
Show more >We study different operator radii of homomorphisms from an operator algebra into B(H) and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if Ω is a K-spectral set for a Hilbert space operator, then it is a M-numerical radius set, where M = 1/2 (K + K ^{−1}). This is a counterpart of a recent result of Davidson, Paulsen and Woerdeman. More general results for operator radii associated with the class of operators having ρ-dilations in the sense of Sz.-Nagy and Foias are given. A version of a result of Drury concerning the joint numerical radius of non-commuting n-tuples of operators is also obtained.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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Source :
Submission date :
2025-01-24T17:31:23Z
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