0000000000740831
AUTHOR
J Guillen
Property (gR) and perturbations
Property (gR) holds for a bounded linear operator T defined on a complex Banach space X, 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 B-Browder. In this paper we consider the permanence of this property under nilpotent, perturbations commuting with T.
Property (gb) through local spectral theory
Property (gb) for a bounded linear operator T on a Banach space X means that the points c of the approximate point spectrum for which c I-T is upper semi B-Weyl are exactly the poles of the resolvent. In this paper we shall give several characterizations of property (gb). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gb) holds for large classes of operators and prove the stability of property (gb) under some commuting perturbations.