Abstract
Let \(\mathcal {H}\) be an infinite dimensional separable complex Hilbert space and \(\mathcal {B(H)}\) the algebra of all bounded linear operators on \(\mathcal {H}\). In this paper, we characterize some features of the topological uniform descent resolvent set \(\rho _\tau (T)\) for an operator \(T\in \mathcal {B(H)}\), and give a classification of the components of \(\rho _\tau (T)\). Then using topological uniform descent spectrum and \(\rho _\tau (T)\), we discuss the SVEP and further characterize those operators for which the SVEP is preserved under compact perturbations.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (No. 11701351), the Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ1082) and the Fundamental Research Funds for the Central Universities (No. GK201703008).
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Shi, W. Topological uniform descent and compact perturbations. RACSAM 113, 2221–2233 (2019). https://doi.org/10.1007/s13398-018-0610-0
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DOI: https://doi.org/10.1007/s13398-018-0610-0