Journal of Spectral Theory

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Volume 7, Issue 1, 2017, pp. 137–190
DOI: 10.4171/JST/158

Published online: 2017-03-22

Spectral properties of unbounded $J$-self-adjoint block operator matrices

Matthias Langer[1] and Michael Strauss[2]

(1) University of Strathclyde, Glasgow, UK
(2) University of Sussex, Brighton, UK

We study the spectrum of unbounded $J$ -self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sucient condition for the spectrum being real and derive variational principles for certain real eigenvalues even in the presence of non-real spectrum. The latter lead to lower and upper bounds and asymptotic estimates for eigenvalues.

Keywords: $J$-self-adjoint operator, spectral enclosure, Schur complement, quadratic numerical range, Krein space, spectrum of positive type

Langer Matthias, Strauss Michael: Spectral properties of unbounded $J$-self-adjoint block operator matrices. J. Spectr. Theory 7 (2017), 137-190. doi: 10.4171/JST/158