Fixed point characterization of left amenable Lau algebras (Q1777854)

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.