Abstract
Let \(\cal{H}\) be a complex infinite dimensional Hilbert space and \(\cal{B}(\cal{H})\) be the algebra of all bounded linear operators on \(\cal{H}\). In this paper, we mainly study the operators that satisfy both a-Weyl’s theorem and property (R). Also, the operators whose functional calculus satisfies the two properties are also explored. We give the features for the operator or its functional calculus for which both a-Weyl’s theorem and property (R) hold.
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The authors thank the referee for his several suggestions which have greatly contributed to improve the final form of this article.
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Supported by the National Natural Science Foundation of China (Grant No. 11671201) 1) Corresponding author
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Feng, G.H.Z., Li, P.T. Weyl Type Theorem for Bounded Linear Operator and Its Functional Calculus. Acta. Math. Sin.-English Ser. 40, 528–536 (2024). https://doi.org/10.1007/s10114-023-1249-0
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DOI: https://doi.org/10.1007/s10114-023-1249-0