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

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 .