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Fixed point characterization of left amenable Lau algebras. (English) Zbl 1065.43004
Summary: The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras \(\mathcal{A}\) in terms of left Banach \(\mathcal{A}\)-modules. It also offers an application of this result to some Lau algebras related to a locally compact group \(G\), such as the Eymard-Fourier algebra \(A(G)\), the Fourier-Stieltjes algebra \(B(G)\), the group algebra \(L^1(G)\), and the measure algebra \(M(G)\). In particular, it presents some equivalent statements which characterize the amenability of locally compact groups.

MSC:
43A07 Means on groups, semigroups, etc.; amenable groups
43A10 Measure algebras on groups, semigroups, etc.
43A20 \(L^1\)-algebras on groups, semigroups, etc.
46H05 General theory of topological algebras
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