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

Langer, Matthias and Strauss, Michael (2017) Spectral properties of unbounded J-self-adjoint block operator matrices. Journal of Spectral Theory, 7 (1). pp. 137-190. ISSN 1664-0403

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    Abstract

    We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient 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.