INTERSECTIONS OF SEVERAL DISKS OF THE RIEMANN SPHERE AS K-SPECTRAL SETS

Badea, Catalin; Beckermann, Bernhard; Crouzeix, Michel

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.3934/cpaa.2009.8.37

Title :

INTERSECTIONS OF SEVERAL DISKS OF THE RIEMANN SPHERE AS K-SPECTRAL SETS

Author(s) :

Badea, Catalin [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Beckermann, Bernhard [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Crouzeix, Michel [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]

Journal title :

Communications on Pure and Applied Mathematics

Pages :

37-54

Publisher :

Wiley

Publication date :

2009

ISSN :

0010-3640

English keyword(s) :

Spectral set
complete K-spectral set
intersection of spectral sets
normal dilation

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

We prove that if n closed disks D-1, D-2,...,Dn, of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then their intersection D-1 boolean AND D-2 boolean AND ... boolean AND D-n is a ...
Show more >We prove that if n closed disks D-1, D-2,...,Dn, of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then their intersection D-1 boolean AND D-2 boolean AND ... boolean AND D-n is a complete K-spectral set for A, with K <= n + n(n-1)/root 3. When n = 2 and the intersection X-1 boolean AND X-2 is an annulus, this esult gives a positive answer to a question of A.L. Shields (1974).Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

0807.3136
Open access
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