Generalized Weyl's theorem for functions of operators and compact perturbations
Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 899-910
https://doi.org/10.4134/BKMS.2012.49.5.899
Printed September 30, 2012
Ting Ting Zhou, Chun Guang Li, and Sen Zhu
Jilin University, Jilin University, Jilin University
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
MSC numbers : Primary 47A10, 47A60; Secondary 47A53, 47A58
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