Preservation results for new spectral properties

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Preservation results for new spectral properties

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Title: Preservation results for new spectral properties
Author: Zariouh, Hassan
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.
Date: 2015

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