Relatively Bounded Perturbations of a Closed Linear Relation and Its Adjoint
Guixin Xu · Discrete Dynamics in Nature and Society · 2022
This paper is concerned with the relatively bounded perturbations of a closed linear relation and its adjoint in Hilbert spaces. A stability result about orthogonal projections onto the ranges of linear relations is obtained. By using this result, two perturbation theorems for a closed relation and its adjoint are given. These results generalize the corresponding results for single‐valued linear operators to linear relations and some of which weaken certain assumptions of the related existing results.