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

Abstract

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.