Property (R) under perturbations

Property (R) holds for a bounded linear operator T defined on a complex Banach space X, if the isolated points of the spectrum of T which are eigenvalues of finite multiplicity are exactly those points c of the approximate point spectrum such CI- T is upper semi-Browder. In this paper we consider the permanence of this property under quasi nilpotent, Riesz or algebraic perturbations commuting with T.