Property (R) under Perturbations

Property ( R ) holds for a bounded linear operator , defined on a complex infinite dimensional Banach space X , if the isolated points of the spectrum of T which are eigenvalues of finite multiplicity are exactly those points λ of the approximate point spectrum for which λ I − 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 .