Stability of Self-Adjoint Extensions of Symmetric Linear Relations under Relatively Bounded Perturbations on Hilbert Spaces

Paper Details

Authors: Kito S.L.; Wanjala G.

DOI: 10.28924/2291-8639-24-2026-131

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 0

Abstract

We investigate the stability of self-adjoint extensions of a closed symmetric linear relation S when subjected to a relatively bounded perturbation by another symmetric linear relation T. We demonstrate that the deficiency indices of S are stable under such perturbations, provided the relative bound is small enough. This result is fundamental, as it ensures that the perturbed relation S + T possesses the same number of self-adjoint extensions as the original relation S. It is established that if T is relatively bounded with respect to S with a relative bound less than12, then S admits self-adjoint extensions if and only if S + T does. © 2026 the author(s).

Keywords

linear relation; perturbation; self-adjoint; stability

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