Spectral enclosures for a class of block operator matrices

Abstract

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

References in corpus (6)

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• Spectral properties of unbounded J-self-adjoint matrices
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Cited by in corpus (2)

• On classification of singular matrix difference equations of mixed order
• On a class of non-Hermitian matrices with positive definite Schur complements