# On the stability of self-adjointness of linear relations

## TL;DR

This paper investigates how the property of self-adjointness in linear relations within Hilbert spaces remains stable under certain perturbations, extending known results from linear operators to more general relations.

## Contribution

It generalizes existing stability results for self-adjointness from linear operators to linear relations and relaxes some of the previous conditions required.

## Key findings

- Self-adjoint relations remain stable under bounded perturbations.
- Relatively bounded perturbations also preserve self-adjointness.
- The paper broadens the applicability of stability results to linear relations.

## Abstract

This paper focuses on the stability of self-adjointness of linear relations under perturbations in Hilbert spaces. It is shown that a self-adjoint relation is still self-adjoint under bounded and relatively bounded perturbations. The results obtained in the present paper generalize the corresponding results for linear operators to linear relations, and some weaken the conditions of the related existing results.