Extended Weyl theorems and perturbations - Rashid, M. H. M. (Methods of Functional Analysis and Topology, 2013)
In this paper we study the properties ( gaw), (aw), ( gab) and (ab), a variant of Weyl’s type theorems introduced by Berkani. We established for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which the properties (gaw), (aw), ( gab) and (ab) hold. Among other things, we study the stability of the properties ( gaw), (aw), ( gab) and (ab) for a polaroid operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T.