Continuity of Convolution and SIN Groups

被引：2

作者：

Pachl, Jan ^{[1
]}

Steprans, Juris ^{[2
]}

机构：

[1] Fields Inst, 222 Coll St, Toronto, ON M5T 3J1, Canada

[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2017年 / 60卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

topological group; SIN property; measure algebra; convolution; UNIFORMLY CONTINUOUS-FUNCTIONS; LOCALLY COMPACT-GROUPS; TOPOLOGICAL-GROUPS;

D O I：

10.4153/CMB-2017-002-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 SIN property. On the larger space LUC(G)*, which includes the measure algebra, convolution is also jointly continuous if and only if the group has the SIN property, but not separately continuous for many non-SIN groups.

引用

页码：845 / 854

页数：10

共 15 条

[1]

[Anonymous], 1989, ANAL SEMIGROUPS FUNC

[2]

[Anonymous], 2006, U LECT SERIES

[3]

Bogachev VI., 2007, MEASURE THEORY, VI, II

[4] On the topological centre of the algebra LUC (G)* for general topological groups [J].