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Continuity of Convolution and SIN Groups

Published online by Cambridge University Press:  20 November 2018

Jan Pachl  and
Juris Steprans
Jan Pachl
Affiliation:
Fields Institute, 222 College Street, Toronto, ON M5T 3J1 e-mail: jan.pachl@utoronto.ca
Juris Steprans
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3 e-mail: steprans@yorku.ca
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Abstract

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Let the measure algebra of a topological group $G$ 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 $G$ has the $\text{SIN}$ property. On the larger space $\text{LUC}{{(G)}^{*}}$, which includes the measure algebra, convolution is also jointly continuous if and only if the group has the $\text{SIN}$ property, but not separately continuous for many non-SIN groups.

Keywords

43A1022A10topological groupSIN propertymeasure algebraconvolution
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 4 , 01 December 2017 , pp. 845 - 854
Copyright
Copyright © Canadian Mathematical Society 2017

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