Fixed point characterization of left amenable Lau algebras

Abstract

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 𝒜 in terms of left Banach 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 L1(G), and the measure algebra M(G). In particular, it presents some equivalent statements which characterize amenability of locally compact groups.