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Generalized Weyl's theorem and hyponormal operators

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

M. Berkani  and
A. Arroud
A. Arroud
Affiliation:
Groupe d'Analyse et Théorie des Opérateurs (G.A.T.O) Université Mohammed IFaculté des Sciences Département de Mathématiques Oujda Morocco, e-mail: berkani@sciences.univ-oujda.ac.maarroud@sciences.univ-oujda.ac.ma
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Abstract

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Let T be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of T is the set σBW(T) of all λ ∈ Сsuch that T − λI is not a B-Fredholm operator of index 0. Let E(T) be the set of all isolated eigenvalues of T. The aim of this paper is to show that if T is a hyponormal operator, then T satisfies generalized Weyl's theorem σBW(T) = σ(T)/E(T), and the B-Weyl spectrum σBW(T) of T satisfies the spectral mapping theorem. We also consider commuting finite rank perturbations of operators satisfying generalized Weyl's theorem.

Keywords

B-Fredholm operatorB-Weyl spectrumgeneralized Weyl's theorem

MSC classification

Secondary: 47A53: (Semi-) Fredholm operators; index theories 47A55: Perturbation theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 2 , April 2004 , pp. 291 - 302
Copyright
Copyright © Australian Mathematical Society 2004

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