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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 62, Pages 3333-3338
http://dx.doi.org/10.1155/S0161171204310446

Fixed point characterization of left amenable Lau algebras

Department of Mathematics, Isfahan University of Technology, Isfahan, Iran

Received 1 October 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.