Abstract
Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl’s theorem, where f ∊ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl’s theorem for f(T).
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Supported by the Fundamental Research Funds For the Central Universities (Grant No. 2016CSY020), the National Natural Science Foundation of China (Grant No. 11701351) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2018JQ1082)
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Dong, J., Cao, X.H. & Dai, L. On Weyl’s Theorem for Functions of Operators. Acta. Math. Sin.-English Ser. 35, 1367–1376 (2019). https://doi.org/10.1007/s10114-019-7512-8
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DOI: https://doi.org/10.1007/s10114-019-7512-8