Publisher DOI: 10.1016/j.jmaa.2021.125985
arXiv ID: 2110.01244v2
Title: On equicontinuity and tightness of bi-continuous semigroups
Language: English
Authors: Kruse, Karsten  
Schwenninger, Felix 
Keywords: Bi-continuous semigroup; Tight; Equicontinuous; Mixed topology; C-sequential
Issue Date: 6-Jan-2022
Source: Journal of Mathematical Analysis and Applications (in Press): 125985 (2022)
Abstract (english): 
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.
ISSN: 1096-0813
Journal: Journal of mathematical analysis and applications 
Institute: Mathematik E-10 
Document Type: Article
Project: Modellierung, Simulation und Optimierung mit fluiddynamischen Anwendungen 
Peer Reviewed: Yes
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