Ruan, Zhong-Jin The operator amenability of \(A(G)\). (English) Zbl 0842.43004 Am. J. Math. 117, No. 6, 1449-1474 (1995). Let \(G\) be a locally compact group and \(A(G)\) its Fourier algebra. The main results in this paper are: (1) \(A(G)\) is operator amenable for every compact group \(G\); (2) the group \(G\) is amenable if and only if \(A(G)\) is operator amenable; (3) the \(C^*\)-algebra \(A\) is Banach algebra amenable if and only if \(A\) is operator amenable. Reviewer: A.G.Baskakov (Voronezh) Cited in 10 ReviewsCited in 52 Documents MSC: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 22D15 Group algebras of locally compact groups Keywords:locally compact group; Fourier algebra; operator amenable; amenable PDFBibTeX XMLCite \textit{Z.-J. Ruan}, Am. J. Math. 117, No. 6, 1449--1474 (1995; Zbl 0842.43004) Full Text: DOI