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On equicontinuity and tightness of bi-continuous semigroups
Publikationstyp
Journal Article
Date Issued
2022-05-15
Sprache
English
Author(s)
Institut
Volume
509
Issue
2
Article Number
125985
Citation
Journal of Mathematical Analysis and Applications 509 (2): 125985 (2022-05-15)
Publisher DOI
Scopus ID
ArXiv ID
Peer Reviewed
true
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.
Subjects
Bi-continuous semigroup
Tight
Equicontinuous
Mixed topology
C-sequential
DDC Class
510: Mathematik