Perturbations of Positive Semigroups on AM-Spaces

TL;DR

This paper investigates how positive perturbations affect positive semigroups on AM-spaces, extending known results from AL-spaces and applying findings to unbounded perturbations of the shift semigroup.

Contribution

It provides a dual counterpart to Desch's perturbation theorem for AL-spaces, specifically for AM-spaces, and explores unbounded perturbations of the shift semigroup.

Findings

Established a dual perturbation result for AM-spaces

Extended perturbation theory to unbounded shift semigroup perturbations

Connected perturbation results between AM- and AL-spaces

Abstract

We consider positive perturbations of positive semigroups on AM-spaces and prove a result which is the dual counterpart of a famous perturbation result of Desch in AL-spaces. As an application we consider unbounded perturbations of the shift semigroup.