B-Weyl spectrum and poles of the resolvent

[摘要] Let T be a bounded linear operator acting on a Banach space and let sigma(BW)(T) = {lambda is an element of C such that T - lambdaI is not a B-Fredholm operator of index 0} be the B-Weyl spectrum of T. Define also E (T) to be the set of all isolated eigenvalues in the spectrum sigma (T) of T, and Pi(T) to be the set of the poles of the resolvent of T. In this paper two new generalized versions of the classical Weyl's theorem are considered. More precisely, we seek for conditions under which an operator T satisfies the generalized Weyl's theorem: sigma(BW)(T) = (T)\E(T), or the version II of the generalized Weyl's theorem: sigma(BW)(T) = sigma(T)\Pi(T). (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-08-15