Stability of Property (gm) under Perturbation and Spectral Properties Type Weyl Theorems

[摘要] A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

[学科分类] 计算机应用

[关键词] Weyl’s theorem;Weyl spectrum;polaroid operators;property (gm);property (m).