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 X 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.