Generalized Weyl's theorem and quasi-affinity

Pietro Aiena¹ ; Mohammed Berkani²

¹ Dipartimento di Metodi e Modelli Matematici Facoltà di Ingegneria Università di Palermo Viale delle Scienze I-90128 Palermo, Italy
² Département de Mathématiques Faculté des Sciences Université Mohammed I Oujda, Morocco

Studia Mathematica, Tome 198 (2010) no. 2, pp. 105-120

Résumé

A bounded operator $T\in L(X)$ acting on a Banach space $X$ is said to satisfy generalized Weyl's theorem if the complement in the spectrum of the B-Weyl spectrum is the set of all eigenvalues which are isolated points of the spectrum. We prove that generalized Weyl's theorem holds for several classes of operators, extending previous results of Istrăţescu and Curto–Han. We also consider the preservation of generalized Weyl's theorem between two operators $T\in L(X)$, $S\in L(Y)$ intertwined or asymptotically intertwined by a quasi-affinity $A\in L(X,Y)$.

Détail

DOI : 10.4064/sm198-2-1

Keywords: bounded operator acting banach space said satisfy generalized weyls theorem complement spectrum b weyl spectrum set eigenvalues which isolated points spectrum prove generalized weyls theorem holds several classes operators extending previous results istr escu curto han consider preservation generalized weyls theorem between operators intertwined asymptotically intertwined quasi affinity