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On Lau's conjecture II


Author: Khadime Salame
Journal: Proc. Amer. Math. Soc. 148 (2020), 1999-2008
MSC (2010): Primary 47H10, 47H20; Secondary 43A07
DOI: https://doi.org/10.1090/proc/14893
Published electronically: January 29, 2020
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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.


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Additional Information

Khadime Salame
Affiliation: Diourbel, Senegal
Email: khadime.salame1313@gmail.com

DOI: https://doi.org/10.1090/proc/14893
Keywords: Amenability, nonexpansive mappings, left uniformly continuous function, semigroup, weak* topology.
Received by editor(s): July 24, 2019
Published electronically: January 29, 2020
Dedicated: This paper is dedicated to Khadime Rassoul (PBUH) for his courage and bravery
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2020 American Mathematical Society