Sun dual theory for bi-continuous semigroups

TL;DR

This paper extends the concept of sun dual spaces to bi-continuous semigroups, providing a new theoretical framework that generalizes classical duality results under mild topological assumptions.

Contribution

It develops a novel theory of sun dual spaces for bi-continuous semigroups, including sun reflexivity and Favard spaces, extending classical results by van Neerven.

Findings

Established a theory for sun dual spaces in bi-continuous semigroups

Extended classical duality results to a broader class of semigroups

Discussed conditions for sun reflexivity and Favard spaces in this setting

Abstract

The sun dual space corresponding to a strongly continuous semigroup is a known concept when dealing with dual semigroups, which are in general only weak$^*$-continuous. In this paper we develop a corresponding theory for bi-continuous semigroups under mild assumptions on the involved locally convex topologies. We also discuss sun reflexivity and Favard spaces in this context, extending classical results by van Neerven.