Some spectral properties of generalized derivations

摘要

Given Banach spaces X and Y and Banach space operators A ∈ L(X ) and B ∈ L(Y), the generalized derivation δ A,B ∈ L(L(Y , X )) is defined by δ A,B (X ) = (L A . R B )(X ) = AX . X B. This paper is concerned with the problem of transferring the left polaroid property, from operators A and B . to the generalized derivation δ A,B . As a consequence, we give necessary and su.cient conditions for δ A,B to satisfy generalized a-Browder's theorem and generalized a- Weyl's theorem. As an application, we extend some recent results concerning Weyl-type theorems.