Perturbations of gaps in the essential spectra of self-adjoint relations

Abstract

This paper is concerned with the stability of gaps in the essential spectra of self-adjoint relations under non-negative relatively compact perturbation in Hilbert spaces. A stability result about semi-boundedness of self-adjoint relations under relatively bounded perturbation is given. It is shown that the gaps in the essential spectra of self-adjoint relations are invariant under non-negative relatively compact perturbation. The results obtained in the present paper generalize the corresponding results for linear operators to linear relations.