PSEUDO SEMI b-FREDHOLM AND GENERALIZED DRAZIN INVERTIBLE OPERATORS THROUGH LOCALIZED SVEP

Abstract

In this paper, we define and study the pseudo upper and lower semi B-Fredholm of bounded operators in a Banach space.  In particular, we prove equality up to S(T) between the left generalized Drazin spectrum and the pseudo upper semi B-Fredholm spectrum, S(T) is the set where T fails to have the SVEP.  Also, we prove that both of the left and the right generalized Drazin operators are invariant under additive commuting power finite rank perturbations and some perturbations for the pseudo upper and lower semi B-Fredholm operators are given.  As applications, we investigate some classes of operators as the supercyclic and multiplier operators.