Continuity of convolution and SIN groups
Functional Analysis
2019-08-15 v3 Group Theory
Abstract
Let the measure algebra of a topological group be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly continuous if and only if the group has the SIN property.
Cite
@article{arxiv.1507.07506,
title = {Continuity of convolution and SIN groups},
author = {Jan Pachl and Juris Steprāns},
journal= {arXiv preprint arXiv:1507.07506},
year = {2019}
}
Comments
8 pages. New in version 3: Updated title, Theorem 4.4 and its corollaries