Rakočević’s property for generalized derivations

Abstract

Given Banach spaces X and Y and Banach space operators A ∈ L(X ) andThis paper is concerned with the problem of the transferring the left polaroid property, from operators A and B * to the generalized derivation δ A,B . As a consequence, we give necessary and sufficient conditions for δ A,B to satisfy generalized a-Browder's theorem and generalized a-Weyl's theorem. As application, we extend some recent results concerning Weyl type theorems.2000 Mathematics Subject Classification. 47A10, 47A53, 47B47.