Open AccessOn Lau’s conjecture II
Author(s) -
Khadime Salame
Publication year - 2020
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14893
Subject(s) - mathematics , conjecture , banach space , semigroup , regular polygon , norm (philosophy) , dual (grammatical number) , pure mathematics , uniformly convex space , fixed point , discrete mathematics , property (philosophy) , combinatorics , mathematical analysis , lp space , eberlein–šmulian theorem , art , philosophy , geometry , literature , epistemology , political science , law
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.