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Perturbation results for Weyl type theorems

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Author(s): M. Berkani | H. Zariouh

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXX;
Issue: 1;
Start page: 119;
Date: 2011;
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Keywords: property ab | property (gab) | property aw | property (gaw) | B-Weyl operators

ABSTRACT
In [12] we introduced and studied properties (gab) and (gaw), which are extensions to the context of B-Fredholm theory, of properties (ab) and (aw) respectively introduced also in [12]. In this paper we continue the study of these properties and we consider their stability under commuting finite rank, compact and nilpotent perturbations. Among other results, we prove that if T is a bounded linear operator acting on a Banach space X, then T possesses property (gaw) if and only if T satisfies generalized Weyl's theorem and E(T) = Ea(T). We prove also that if T possesses property ab or property (aw) or property (gaw) respectively, and N is a nilpotent operator commuting with T, then T+N possesses property ab or property aw or property (gaw) respectively. The same result holds for property (gab) in the case of a-polaroid operators.
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