A Desch-Schappacher perturbation theorem for bi-continuous semigroups

Christian, Budde and Farkas, Bálint (2018) A Desch-Schappacher perturbation theorem for bi-continuous semigroups. MATHEMATISCHE NACHRICHTEN, 293 (6). pp. 1053-1073. ISSN 0025-584X

Preview

Text 1811.08455.pdf Available under License Creative Commons Attribution. Download (300kB) | Preview

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.

Actions (login required)

Edit Item