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Dual multiplier Banach algebras and Connes-amenability. (English) Zbl 1349.46049
From the authors’ abstract: “…we consider a Banach algebra $$B$$ for which the multiplier algebra $$M(B)$$ is a dual algebra in sense of V. Runde [Stud. Math. 148, No. 1, 47–66 (2001; Zbl 1003.46028)], and show that under some continuity conditions $$B$$ is amenable if and only if $$M(B)$$ is Connes-amenable. As a result, we conclude that for a discrete amenable group $$G$$, the Fourier-Stieltjes algebra $$B(G)$$ is Connes-amenable if and only if $$G$$ is abelian by finite.” The last term is not explained in the paper. It means that $$G$$ contains an abelian subgroup of finite index.

##### MSC:
 46H20 Structure, classification of topological algebras
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