New Decompositions for Classes of Operators with Topological Uniform Descent

The article describes a new decomposition property for operators with topological uniform descent, like Kato type operators, as well as new results on the stability of this class of operators under perturbations by operators with finite-range power based on topological descent notion, from which we can generalize many perturbation results for a large classes of operators by extending to Banach spaces known techniques on Hilbert spaces. As application of our resuts we obtain that is a lower semi B-Weyl operator if and only if , where is a lower semi B-Browder operator and , for some . Our methods generalize to Banach spaces some results obtained by Aiena for operators acting on Hilbert spaces.

SMALL ESSENTIAL SPECTRAL RADIUS PERTURBATIONS OF OPERATORS WITH TOPOLOGICAL UNIFORM DESCENT

In this paper we consider small essential spectral radius perturbations of operators with topological uniform descent—small essential spectral radius perturbations which cover compact, quasinilpotent and Riesz perturbations.