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On the Schauder fixed point property II

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Abstract

The Schauder fixed point property (F) was introduced and studied by Lau and Zhang as a semigroup formulation in the general setting of convex spaces of the well-known Schauder fixed point theorem in Banach spaces. What amenability property should possess a semigroup or a topological group to satisfy the Schauder fixed point property. Recently, the author provided a partial answer to that question and as a sequel, it is the purpose of this paper to study in more deep this problem. Our main result establishes that for a compact semitopological semigroup S we have: LUC(S) is left amenable if, and only if, S has the fixed point property (F). Furthermore, we also prove that totally bounded topological groups, semitopological groups S with the property that LUC(S) \(\subset \)\({\textrm{aa}}\)(S), and strongly left amenable semitopological semigroups, possess all the Schauder fixed point property.

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Acknowledgements

The author is grateful to the referee for his/her careful reading of the manuscript and useful comments for a better presentation.

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Authors and Affiliations

  1. Departement de Mathematiques, UFR Sciences et Technologies, Universite IBA Der Thiam de Thiès, BP 967, Thiès, Senegal

    Khadime Salame

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  1. Khadime Salame
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Correspondence to Khadime Salame.

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Communicated by Vesko Valov.

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Salame, K. On the Schauder fixed point property II. Ann. Funct. Anal. 14, 78 (2023). https://doi.org/10.1007/s43034-023-00300-1

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  • DOI: https://doi.org/10.1007/s43034-023-00300-1

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