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Spectral inclusion properties of some unbounded block operator matrices. (Chinese. English summary) Zbl 1485.47005

Summary: In this paper, we give Gershgorin’s theorem of the \(2\times 2\) unbounded block operator matrix with bounded off-diagonal entries, and use the spectrum and the numerical range of diagonal entries to investigate the spectral inclusion properties of some unbounded block operator matrices. In particular, for unbounded block operator matrices with symmetric (anti-symmetric) corners, we give more exact localization of spectrum by the quadratic numerical range and Gershgorin’s theorem.

MSC:

47A08 Operator matrices
47A10 Spectrum, resolvent
47A12 Numerical range, numerical radius
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