On Lau’s conjecture II

Abstract

In this paper we are concerned with the study of a long-standing open problem posed by Lau in 1976. This problem is about whether the left amenability property of the space of left uniformly continuous functions of a semitopological semigroup is equivalent to the existence of a common fixed point for every jointly weak* continuous norm nonexpansive action on a nonempty weak* compact convex subset of a dual Banach space. We establish in this paper a positive answer.