Preservation Results for New Spectral Properties

Authors

  • Hassan Zariouh Departement de Mathematiques, Centre Regional pour les Metiers de l'Education et de la Formation de la region de l'Oriental (CRMEFO), Oujda, Morocco

DOI:

https://doi.org/10.17398/

Keywords:

a-Browder's theorem, upper semi-Weyl spectrum, SVEP, Riesz operator

Abstract

A bounded linear operator T is said to satisfy property (SBaw) if 

s_a(T) \ s_SBF (T) = E_a^0 (T)

where s_a(T) is the approximate point spectrum of T;  s_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 (SBb); (SBab) and (SBw). The theory is exemplified in the case of some special classes of operators.

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Published

2015-12-01

Issue

Vol. 30 No. 2 (2015)

Section

Operator Theory

How to Cite

Preservation Results for New Spectral Properties. (2015). Extracta Mathematicae, 30(2), 191-205. https://doi.org/10.17398/