A Desch–Schappacher perturbation theorem for bi‐continuous semigroups. Issue 6 (4th May 2020)

• Record Type: Journal Article
• Authors: Budde, Christian; Farkas, Bálint
• Is Part Of: Mathematische Nachrichten. Volume 293:Issue 6(2020)
• Page Start: 1053
• Page End: 1073
• Publication Date: 2020-05-04
• Subjects: bi‐continuous semigroups -- Desch–Schappacher type perturbation -- extrapolation spaces -- implemented semigroups; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201800534
• Languages: English
• ISSNs: 0025-584X

Abstract

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.