Qi, Yaru; Huang, Junjie; Alatancang Spectral inclusion properties of some unbounded block operator matrices. (Chinese. English summary) Zbl 1485.47005 Sci. Sin., Math. 44, No. 10, 1099-1110 (2014). 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. Cited in 1 Document MSC: 47A08 Operator matrices 47A10 Spectrum, resolvent 47A12 Numerical range, numerical radius Keywords:unbounded block operator matrix; spectrum; numerical range PDFBibTeX XMLCite \textit{Y. Qi} et al., Sci. Sin., Math. 44, No. 10, 1099--1110 (2014; Zbl 1485.47005) Full Text: DOI