p. 119 - 132 Perturbation results for Weyl type theorems M. Berkani and H. Zariouh Received: June 17, 2010; Accepted: December 12, 2010 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. Keywords: property ab, property (gab), property aw, property (gaw), B-Weyl operators AMS Subject classification: Primary: 47A53, 47A10, 47A11 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2011, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |