SPECTRAL SETS AND OPERATOR RADII

Badea, Catalin; Crouzeix, Michel; Klaja, Hubert

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1112/blms.12191

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

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 >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Frontières de la théorie des opérateurs
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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