Preservation Results for New Spectral Properties

Resumen

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.