The Action of a Left Amenable Semi-topological Semigroup on a Weakly Compact Subset of a Banach Space with Normal Structure
Foad Naderi *
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran.
*Author to whom correspondence should be addressed.
Abstract
Let S be left amenable semi-topological semigroup such that its weak almost periodic compactification Sw is a topological semigroup. We show that every separately continuous, non-expansive and equicontinuous action of S on a weakly compact convex subset of a Banach space with normal structure has a fixed point.
Keywords: Non-expansive mapping, semi-topological semigroup, amenable, left reversible, weakly almost periodic function.