Spectral properties of unbounded J-self-adjoint matrices

TL;DR

This paper investigates the spectral characteristics of unbounded J-self-adjoint block operator matrices, establishing spectral enclosures, conditions for real spectra, and variational principles for eigenvalues, including bounds and asymptotic estimates.

Contribution

It introduces new spectral enclosures, a sufficient condition for real spectra, and variational principles applicable even with non-real spectrum presence.

Findings

Spectral enclosures for unbounded J-self-adjoint matrices

A sufficient condition for the spectrum to be real

Variational principles for eigenvalues with bounds and asymptotic estimates

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.