Berkani, M. and Zariouh, H. (2011) Perturbation results for weyl type theorems. Acta Mathematica Universitatis Comenianae, 80 (1). pp. 119-132.

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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 also prove 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.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48

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