Admissible operators for sun-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 $L^1$.

This is version 3. Minor changes compared to version 2

References in corpus (5)

• Infinite-dimensional input-to-state stability and Orlicz spaces
• On continuity of solutions for parabolic control systems and input-to-state stability
• Neural Field Models with Transmission Delays and Diffusion
• Euclidean structures and operator theory in Banach spaces
• Limit-case admissibility for positive infinite-dimensional systems

Cited by in corpus (1)

• Smoothing of operator semigroups under relatively bounded perturbations