Dual multiplier Banach algebras and Connes-amenability. (English) Zbl 1349.46049

Hayati, Bahman; Amini, Massoud

Publ. Math. 86, No. 1-2, 169-182 (2015).

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.

Reviewer: Wiesław Tadeusz Żelazko (Warszawa)

MSC:

46H20

Structure, classification of topological algebras

Keywords:

amenability; Connes-amenability; dual multiplier algebra; normal virtual diagonal