Abstract
In this paper, we give the Gershgorins theorem of the 2×2 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 the Gershgorins theorem.
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