Abstract
In this paper, some sufficient and necessary conditions for \(T_{B}=\begin{bmatrix}A &{} B\\ 0 &{} D \\ \end{bmatrix}\) in \(\mathcal H \oplus \mathcal K\) to be Kato nonsingular for some closable operator B with \(\mathcal D(B)\supset \mathcal D(D)\) are characterized, where A and D are given closed operators, and \(\mathcal H\) and \(\mathcal K\) are Hilbert spaces. The properties of regular spectrum \(\sigma _{g}(T_{B})\) of closed operator matrix \(T_{B}\) are also studied and some sufficient and necessary conditions for \(\sigma _{g}(T_{B})=\sigma _{g}(A)\cup \sigma _{g}(D)\) are given. In addition, the corresponding properties of regular spectrum of upper triangular Hamiltonian operator matrix are obtained.
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Acknowledgements
We are grateful to the referees for their valuable comments on this paper. This work is supported by National Natural Science Foundation of China (Grant No. 11961022), Natural Science Foundation of Inner Mongolia (Grant Nos. 2022ZD05, 2021MS01017), Basic Scientific Research Funds of Subordinate Universities of Inner Mongolia, Science and Technology Research Project of Inner Mongolia Autonomous University (Grant No. NJZZ23097), Natural Scientific Research Innovation Team of Hohhot Minzu College (Grant No. HM-TD-202005), and Introducing High-level Talents Project of Inner Mongolia.
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Bai, Q., Chen, A. The Regular Spectrum of Upper Triangular Closed Operator Matrices. Mediterr. J. Math. 20, 95 (2023). https://doi.org/10.1007/s00009-023-02308-2
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DOI: https://doi.org/10.1007/s00009-023-02308-2