Journal of Spectral Theory
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Published online: 2017-03-22
Spectral properties of unbounded $J$-self-adjoint block operator matricesMatthias Langer and Michael Strauss (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