Generalized Browder's and Weyl's theorems for Banach space operators

[摘要] We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of a (T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f E H ((T)), the space of functions analytic on an open neighborhood of sigma(T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f (T), for each f is an element of H (sigma(T)). (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] generalized Weyl's theorem;generalized Browder's theorem;algebraically paranormal operator;algebraically M-hyponormal;single valued extension property