Abstract
Let \({\mathcal {H}}\) be a complex infinite dimensional Hilbert space and \(\mathcal {B(H)}\) be the algebra of all bounded linear operators on \({\mathcal {H}}\). \(T\in \mathcal {B(H)}\) is said to satisfy property \((UW_{\Pi })\) if \(\sigma _{a}(T)\setminus \sigma _{ea}(T)=\sigma (T)\setminus \sigma _{D}(T)\), where \(\sigma _{a}(T)\), \(\sigma _{ea}(T)\), \(\sigma (T)\) and \(\sigma _{D}(T)\) denote the approximate point spectrum, the Weyl essential approximate point spectrum, the spectrum and the Drazin spectrum of T, respectively. In this paper, we talk about the property \((UW_{\Pi })\) for functions of operators. Also, the compact perturbations of property \((UW_{\Pi })\) are also discussed.
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This research was supported by the Fundamental Research Funds for the Central Universities (GK 202007002) and the Natural Science Basic Research Plan in Shaanxi Province of China (2021JM-189, 2021JM-519)
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Yang, L., Cao, X. Property \((UW_{\Pi })\) for Functions of Operators and Compact Perturbations. Mediterr. J. Math. 19, 163 (2022). https://doi.org/10.1007/s00009-022-02073-8
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DOI: https://doi.org/10.1007/s00009-022-02073-8