Positive Miyadera-Voigt perturbations of bi-continuous semigroups

TL;DR

This paper investigates positive Miyadera-Voigt perturbations of bi-continuous semigroups on AL-spaces, focusing on the space of bounded Borel measures, and explores their properties within a locally convex topology.

Contribution

It extends Miyadera-Voigt perturbation theory to bi-continuous semigroups on AL-spaces with a new locally convex topology, including measures as a key example.

Findings

Characterization of positive Miyadera-Voigt perturbations

Application to the space of bounded Borel measures

Insights into the structure of bi-continuous semigroups

Abstract

We discuss positive Miyadera-Voigt type perturbations for bi-continuous semigroups on AL-spaces with an additional locally convex topology generated by additive seminorms. Our main example is the space of bounded Borel measures.