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Generalized Weyl's theorem and hyponormal operators

Published online by Cambridge University Press:  09 April 2009

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: [email protected]@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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

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