Property (m) under perturbations

Abstract

A Banach space operator is said to be obeys property (m) if the isolated points of the spectrum σ(T) of T which are eigenvalues of finite multiplicity are exactly those points λ of the spectrum for which T - λ is an upper semi-Browder. In this article, we study the stability of property (m), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, quasi-nilpotent operators, Riesz operator or algebraic operators commuting with T.