Property (ω) and topological uniform descent

Abstract

We give the necessary and sufficient condition for a bounded linear operator with property (ω) by means of the induced spectrum of topological uniform descent, and investigate the permanence of property (ω) under some commuting perturbations by power finite rank operators. In addition, the theory is exemplified in the case of algebraically paranormal operators.

Keywords

Topological uniform descent / consistent in Fredholm and index / property (ω)

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg