Desch-Schappacher Perturbation of One-Parameter Semigroups on Locally Convex Spaces

TL;DR

This paper extends the Desch-Schappacher perturbation theorem to strongly continuous, locally equicontinuous one-parameter semigroups on sequentially complete locally convex spaces, broadening the theoretical framework for such operators.

Contribution

It introduces a new perturbation theorem applicable to a wider class of semigroups on locally convex spaces, generalizing previous results.

Findings

Established a Desch-Schappacher type perturbation theorem for locally convex spaces.

Extended the applicability of perturbation results to sequentially complete locally convex spaces.

Provided theoretical foundations for future research on semigroup perturbations in functional analysis.

Abstract

We prove a Desch-Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one-parameter semigroups which are defined on a sequentially complete locally convex space.