Abstract
In this paper we are dealing with the question on what amenability property should possess a semigroup to ensure it has the Schauder fixed point property. We provide a positive answer to this problem for the class \(\Sigma \)-ELA of all n-extremely left amenable semitopological semigroups. As an application, we derive partial answers (for \(\Sigma \)-ELA, locally finite groups, and semidirect product of \(\Sigma \)-ELA semigroups) to an open problem posted by Lau in 1976 (Lau, Fixed point theory and its applications, Academic Press, Orlando, 1976)
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Acknowledgements
This paper was written during a short stay of the author in Edmonton. The author would like to thank Serigne Anbdoul Ahad Sene and Serigne Saliou Fall for their kind hospitality. The author is also grateful to the referee for his/her careful reading of the paper and useful suggestions.
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Communicated by Volker Runde.
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Salame, K. On the Schauder fixed point property. Ann. Funct. Anal. 11, 1–16 (2020). https://doi.org/10.1007/s43034-019-00016-1
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DOI: https://doi.org/10.1007/s43034-019-00016-1