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

  • Zhou, Ting Ting ;
  • Li, Chun Guang ;
  • Zhu, Sen
  • Received : 2011.04.29
  • Published : 2012.09.30

Abstract

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

Keywords

generalized Weyl's theorem;operator approximation;compact perturbations

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