2002/11/30 by Brian E. Forrest, Volker Runde · 1 citation
Mathematics · #math.FA #math.OA #msc:22D25 #msc:22E99 #msc:43A30 #msc:46H20 #msc:46H25 #msc:47L50
published as Math. Z. 250 (2005), 731-744 · 16 pages; some, hopefully clarifying revisions
arxiv created 2004/04/28 · arxiv updated 2009/11/30
Let G be a locally compact group. We show that its Fourier algebra A(G) is amenable if and only if G has an abelian subgroup of finite index, and that its Fourier-Stieltjes algebra B(G) is amenable if and only if G has a compact, abelian subgroup of finite index. We then show that A(G) is weakly amenable if the component of the identity of G is abelian, and we prove some partial results towards the converse.