Admissible operators for sun-dual semigroups

TL;DR

This paper extends duality results for semigroups to cases with sun-dual frameworks, broadening the scope of admissibility testing for various state spaces.

Contribution

It introduces an extension of classical duality results to sun-dual semigroups without strong continuity, enabling broader admissibility analysis.

Findings

Extended duality results to sun-dual semigroups

Broader admissibility testing for continuous functions and L^1 spaces

Applicable to non-strongly continuous dual semigroups

Abstract

We extend classical duality results by Weiss on admissible operators to settings where the dual semigroup lacks strong continuity. This is possible using the sun-dual framework, which is not immediate from the duality of the input and output maps. This extension enables the testing of admissibility for a broader range of examples, in particular for state space of continuous functions or $L^1$.