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Continuity of Convolution and SIN Groups
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- Journal:
- Canadian Mathematical Bulletin / Volume 60 / Issue 4 / 01 December 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 845-854
- Print publication:
- 01 December 2017
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- Article
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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.
