Nonexpansive retractions and fixed point properties

Among other results, we prove that if a dual Banach space E has the weak⁎ fixed point property, then E has the weak⁎ fixed point property for commuting separable semitopological semigroups of nonexpansive mappings and study the existence of ergodic retractions for right amenable semigroups and commuting families of nonexpansive mappings. This answers an open problem of Lau and Mah (1976) [12] for commuting separable semi-topological semigroups.