Fixed point set of semigroups of non-expansive mappings and amenability

In this paper, we study the fixed point set of a strongly continuous non-expansive semigroup S = {T (t): t ∈ S} of a semitopological semigroup S for which CB(S) is n-extremely left amenable. Also, we study the fixed point set of a strongly continuous semigroup of mappings when S is a semigroup which is a sub-semigroup of a locally convex topological vector space with addition. Some applications to harmonic analysis are also provided. © 2007 Elsevier Inc. All rights reserved