Property \((R)\) under perturbations (Q1943586)

In this paper, the authors show the permanence of property (R), satisfied by an operator \(T\) acting in an infinite dimensional complex Banach space, under quasi-nilpotent, Riesz, or algebraic perturbations commuting with \(T\). Such an operator \(T\) is said to satisfy property (R) when the isolated points of its spectrum which are eigenvalues of finite multiplicity are exactly those points \(\lambda\) of its approximate point spectrum for which \(\lambda I-T\) is upper semi-Browder.