Fixed point properties for semigroups on weak$^{*}$ closed sets of dual Banach spaces

Abstract

We study the long-standing problem as to when a left reversible semitopological semigroup $S$ acting as nonexpansive mappings on a weak$^{*}$ closed convex subset $K$ of the dual space $E^*$ of a Banach space $E$ has a common fixed point in $K$. We show t