Preservation results for new spectral properties

Abstract

A bounded linear operator T is said to satisfy property (S Baw) if (σ_a (T) ) ⁄σ_(SBF_+^- ) (T) = E_a^0(T); where σ_a(T) is the approximate point spectrum of T; σ_(SBF_+^- ) (T) is the upper semi-B-Weyl spectrum of T and E_a^0(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in its approximate point spectrum. In this paper we give a characterization of this spectral property for a bounded linear operator having SVEP on the complementary of its upper semi-B-Weyl spectrum, and we study its stability under commuting Riesz-type perturbations. Analogous results are obtained for the properties (S Bb); (S Bab) and (S Bw): The theory is exemplified in the case of some special classes of operators.