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

2003/10/31 by Volker Runde
Mathematics · #math.FA #math.OA #msc:22A15 #msc:22A20 #msc:43A07 #msc:43A10 #msc:43A60 #msc:46H20 #msc:46H25 #msc:46M18 #msc:46M20

paper · pdf

published as Trans. Amer. Math. Soc. 358 (2006), 391-402 · 16 pages; some more, minor revisions

arxiv created 2004/06/01 · arxiv updated 2009/12/01

Abstract

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)^∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)^∗ is an example of a Connes-amenable, dual Banach algebra without a normal,virtual diagonal.

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