Abstract
Property (R) holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. Let \(A\in\cal{B}(\cal{H})\) and \(B\in\cal{B}(\cal{K})\), where \(\cal{H}\) and \(\cal{K}\) are complex infinite dimensional separable Hilbert spaces. We denote by MC the operator acting on \(\cal{H}\oplus\cal{K}\) of the form \({M_C} = \left( {\begin{array}{*{20}{c}} A&C \\ 0&B \end{array}} \right)\). In this paper, we give a sufficient and necessary condition for MC ∈ (R) for all \(C\in\cal{B}(\cal{K},\cal{H})\).
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Supported by the Fundamental Research Funds for the Central Universities (Grant No. GK 202007002) and Nature Science Basic Research Plan in Shaanxi Province of China (Grant No. 2021JM-189, 2021JM-519)
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Yang, L.L., Cao, X.H. Property (R) for Upper Triangular Operator Matrices. Acta. Math. Sin.-English Ser. 39, 523–532 (2023). https://doi.org/10.1007/s10114-023-1306-8
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DOI: https://doi.org/10.1007/s10114-023-1306-8