A Desch–Schappacher perturbation theorem for bi‐continuous semigroups

Christian Budde and Bálint Farkas

Mathematische Nachrichten, 2020, vol. 293, issue 6, 1053-1073

Abstract: We prove a Desch–Schappacher type perturbation theorem for one‐parameter semigroups on Banach spaces which are not strongly continuous for the norm, but possess a weaker continuity property. In this paper we chose to work in the framework of bi‐continuous semigroups. This choice has the advantage that we can treat in a unified manner two important classes of semigroups: implemented semigroups on the Banach algebra L(E) of bounded, linear operators on a Banach space E, and semigroups on the space of bounded and continuous functions over a Polish space induced by jointly continuous semiflows. For both of these classes we present an application of our abstract perturbation theorem.

Date: 2020
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https://doi.org/10.1002/mana.201800534

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