GENERALIZED WEYL'S THEOREM FOR FUNCTIONS OF OPERATORS AND COMPACT PERTURBATIONS

Title & Authors
GENERALIZED WEYL'S THEOREM FOR FUNCTIONS OF OPERATORS AND COMPACT PERTURBATIONS
Zhou, Ting Ting; Li, Chun Guang; Zhu, Sen;

Abstract
Let $\small{\mathcal{H}}$ be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on $\small{\mathcal{H}}$ to satisfy that $\small{f(T)}$ obeys generalized Weyl's theorem for each function $\small{f}$ analytic on some neighborhood of $\small{{\sigma}(T)}$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.
Keywords
generalized Weyl's theorem;operator approximation;compact perturbations;
Language
English
Cited by
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