J. Aust. Math. Soc.  76 (2004), 291-302
Generalized Weyl's theorem and hyponormal operators

M. Berkani
  Groupe d'Analyse et Théorie des Opérateurs (G.A.T.O.)
  Université Mohammed I
  Faculté des Sciences
  Département de Mathématiques
  Oujda
  Morocco
  berkani@sciences.univ-oujda.ac.ma
and
A. Arroud
  Groupe d'Analyse et Théorie des Opérateurs (G.A.T.O.)
  Université Mohammed I
  Faculté des Sciences
  Département de Mathématiques
  Oujda
  Morocco
  arroud@sciences.univ-oujda.ac.ma


Abstract
Let $T$ be a bounded linear operator acting on a Hilbert space $H$. The $B$-Weyl spectrum of $T$ is the set $\sigma_{BW}(T)$ of all $\lambda\in\mathbb{C}$ such that $T-\lambda I$ 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 $\sigma_{BW}(T) = \sigma(T) \backslash E(T)$, and the $B$-Weyl spectrum $\sigma_{BW}(T)$ of $T$ satisfies the spectral mapping theorem. We also consider commuting finite rank perturbations of operators satisfying generalized Weyl's theorem.
Download the article in PDF format (size 100 Kb)
TeXAdel Scientific Publishing ©  Australian MS