On Lau’s conjecture II | Zendy

Khadime Salame | Zendy

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On Lau’s conjecture II

Author(s) -

Khadime Salame

Publication year - 2019

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.

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