Spectral enclosures for a class of block operator matrices

Giribet, Juan and Langer, Matthias and Martínez Pería, Francisco and Philipp, Friedrich and Trunk, Carsten (2020) Spectral enclosures for a class of block operator matrices. Journal of Functional Analysis, 278 (10). 108455. ISSN 0022-1236 (https://doi.org/10.1016/j.jfa.2019.108455)

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We prove new spectral enclosures for the non-real spectrum of a class of 2×2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.