TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values μ(f) where μ runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. The main purpose of this paper is to prove a topological analogue (which is also a generalization) of this theorem for locally compact semigroups.