Amenable locally compact semigroups and a fixed point property

Abstract

Abstract. For a locally compact semigroup S, we study a general fixed point property in terms of Banach left S-modules. We then use this property to give our main result which is a new characterization for left amenability of a large class of locally compact semigroups; finally, we investigate several examples which lead us to the conjecture that the main result remains true for all locally compact semigroups. Key Words and Phrases: Banach left S-module, foundation semigroup, left amenability, left fixed point, left invariant mean, locally compact semigroup, weak * -operator topology.