On equicontinuity and tightness of bi-continuous semigroups

Abstract

In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology. This paper aims to give minimal assumptions in order to recover typical features like tightness and equicontinuity with respect to the mixed topology as well as to carefully clarify on mutual relations between previously studied variants of these notions. The abstract results -- exploiting techniques from topological vector spaces -- are thoroughly discussed by means of several example classes, such as semigroups on spaces of bounded continuous functions.

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Cited by in corpus (6)

• Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups
• A note on the Lumer--Phillips theorem for bi-continuous semigroups
• Mixed topologies on Saks spaces of vector-valued functions
• Weighted composition semigroups on spaces of continuous functions and their subspaces
• Sun dual theory for bi-continuous semigroups
• The abstract Cauchy problem in locally convex spaces