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

• Zhou, Ting Ting (Institute of Mathematics Jilin University) ;
• Li, Chun Guang (Institute of Mathematics Jilin University) ;
• Zhu, Sen (Department of Mathematics Jilin University, School of Mathematical Sciences Fudan University)
• 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.

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