Sun dual theory for bi-continuous semigroups

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${}^{\ast }$-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.

References in corpus (2)

• On equicontinuity and tightness of bi-continuous semigroups
• Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups