Perturbation theory for selfadjoint relations

TL;DR

This paper develops perturbation theorems for selfadjoint relations, analyzing how their spectra change under finite-rank perturbations, extending classical results to a broader relation framework.

Contribution

It introduces Weyl-type perturbation results for selfadjoint relations and provides a detailed spectral analysis under finite-rank perturbations.

Findings

Established perturbation bounds for spectra of selfadjoint relations.

Analyzed spectral changes due to finite-rank perturbations.

Extended classical spectral perturbation results to the relation setting.

Abstract

We study Weyl-type perturbation theorems in the context of linear closed relations. We establish general results on perturbations for dissipative relations. In the particular case of selfadjoint relations, we study finite-rank perturbations and carry out a detailed analysis of the corresponding changes in the spectrum.