Perturbations of Weyl’s Theorems for Unbounded Class-A Operators

Abstract

The significance of Weyl's spectrum is regional to the perturbation theory but recently it is related to operator theory in some theorems. The study of Weyl’s theorem has so far limited to the class of bounded operators, however, lately this study has been extended to some classes of unbounded operators such as hypanormal, posinormal and class- operators. The aim of this article is to continue study more spectral properties for class-  operators. First, we use property  to study property (b) and then show the equivalent of property (gb) with property (gw). Secondly, we start to study new spectral properties that was defined for bounded operators we start with  and  properties and show that for any operator that belongs to class-  will possess them. Finally, we resuming our goal and give our last two properties  and  and prove them for , also we established the connection between these properties.