Positive Desch-Schappacher perturbations of bi-continuous semigroups on $\mathrm{AM}$-spaces

TL;DR

This paper studies how positive Desch-Schappacher perturbations affect bi-continuous semigroups on AM-spaces, with applications to translation semigroups and operator spaces, expanding understanding of perturbation effects in functional analysis.

Contribution

It introduces the analysis of positive Desch-Schappacher perturbations for bi-continuous semigroups on AM-spaces, including specific examples involving translation and operator semigroups.

Findings

Perturbation preserves positivity of semigroups.

Application to translation semigroups on function spaces.

Application to bounded linear operator semigroups.

Abstract

In this paper, we consider positive Desch-Schappacher perturbations of bi-continuous semigroups on $\mathrm{AM}$-spaces with an additional property concerning the additional locally convex topology. As an examples, we discuss perturbations of the left-translation semigroup on the space of bounded continuous function on the real line and on the space of bounded linear operators.