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 algebras𝒜in terms of left Banach𝒜-modules. It also offers an application of this result to some Lau algebras related to a locally compact groupG, such as the Eymard-Fourier algebraA(G), the Fourier-Stieltjes algebraB(G), the group algebraL1(G), and the measure algebraM(G). In particular, it presents some equivalent statements which characterize amenability of locally compact groups.