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arXiv · 1811.08455

A Desch-Schappacher perturbation theorem for bi-continuous semigroups

Christian Budde·Bálint Farkas
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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 $\mathscr{L}(E)$ 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

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Christian Budde, Bálint Farkas. 2018-11-20. A Desch-Schappacher perturbation theorem for bi-continuous semigroups. https://doi.org/10.1002/mana.201800534

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