Abstract
In this paper we investigate the block numerical range and the existences of estimable decompositions of bounded linear operators on a separable Hilbert space. By using spectral measure, we show that there exists an estimable decomposition for the spectrum of every bounded normal operator. Furthermore, the corresponding result also holds for hyponormal operators with totally disconnected spectra. Finally, we obtain that for spectral operator, there exists an estimable decomposition, under quasi-nilpotent equivalence.
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Acknowledgements
The authors are grateful to the referees for valuable comments on this paper. The work of the first and second authors is supported by the National Nature Science Foundation of China (Grant Number 11761029).
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Communicated by Jussi Behrndt.
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This article is part of the topical collection “Spectral Theory and Operators in Mathematical Physics” edited by Jussi Behrndt, Fabrizio Colombo and Sergey Naboko.
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Yu, J., Chen, A. & Wu, J. Block Numerical Range and Estimable Decomposition of Some Hyponormal Operators. Complex Anal. Oper. Theory 14, 39 (2020). https://doi.org/10.1007/s11785-019-00967-2
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DOI: https://doi.org/10.1007/s11785-019-00967-2