The property $ (\omega{ \pi }) $ as a generalization of the a-Weyl theorem

Abstract

<p>In this paper, for a bounded linear operator defined on a complex Banach space of infinite dimension, we consider the set of isolated points in its approximate point spectrum, which are eigenvalues of finite multiplicity; this set can be equal to the spectrum of the operator but without its upper semi-Fredholm spectrum, and this relation or equality defines in the literature a new spectral property called the property $ (\omega{ \pi }) $ and is a generalization of the classical a-Weyl theorem. We establish some characterizations and consequences about the property $ (\omega{ \pi }) $, some with topological aspects. Furthermore, we study this property through the Riesz functional calculus. Part of the spectral structure of a linear operator verifying property $ (\omega{ \pi }) $ is described, obtaining some associated properties.</p>