A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal

Authors:	Volker Runde

Affiliation:	Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Abstract:	Let be a locally compact group, and let denote the space of weakly almost periodic functions on . We show that, if is a -group, but not compact, then the dual Banach algebra $mathcal{WAP}(G)^ast$ does not have a normal, virtual diagonal. Consequently, whenever is an amenable, non-compact -group, $mathcal{WAP}(G)^ast$ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual diagonal. On the other hand, there are amenable, non-compact, locally compact groups such that $mathcal{WAP}(G)^ast$ does have a normal, virtual diagonal.

Keywords:	Locally compact groups Connes-amenability normal virtual diagonals weakly almost periodic functions semigroup compactifications minimally weakly almost periodic groups

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