Abstract
Let \({\mathcal{H}}\) be a complex separable infinite dimensional Hilbert space. In this paper, we characterize those operators T on \({\mathcal{H}}\) satisfying that Weyl’s theorem holds for f(T) for each function f analytic on some neighborhood of σ(T). Also, it is proved that, given an operator T on \({\mathcal{H}}\) and ε > 0, there exists a compact operator K with \({\|K\| < \varepsilon}\) such that Weyl’s theorem holds for T + K.
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Supported by NSF of China (10971079) and the Research Foundation for Young Teachers of Department of Mathematics at Jilin University.
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Li, C.G., Zhu, S. & Feng, Y.L. Weyl’s Theorem for Functions of Operators and Approximation. Integr. Equ. Oper. Theory 67, 481–497 (2010). https://doi.org/10.1007/s00020-010-1796-5
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DOI: https://doi.org/10.1007/s00020-010-1796-5