Common fixed point properties and amenability of a class of Banach algebras

Common fixed point properties and amenability of a class of Banach algebras

Shawn Desaulniers

Rasoul Nasr-Isfahani

Abstract

Let A be a Lau algebra and let S_A be the semigroup of all positive functionals in A with norm one. We obtain some equivalent conditions for left amenability of A in terms of a common fixed point property and the Hahn–Banach property. We then apply these results for certain Lau algebras on a locally compact group G to give characterizations for amenability of G.

Keywords: Lau algebra; Common fixed point property; Left amenability; Fourier algebra; Group algebra; Topological semigroup.