Comptes Rendus
Functional analysis/Dynamical systems
The Ramsey property for Banach spaces and Choquet simplices, and applications
[La propriété de Ramsey des espaces de Banach et des simplexes de Choquet, et applications]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 12, pp. 1242-1246.

Nous montrons que la classe des espaces de Banach de dimension finie et la classe des simplexes de Choquet de dimension finie ont la propriété de Ramsey. En guise d'application, nous montrons que le groupe Aut(G) des isométries linéaires surjectives de l'espace de Gurarij G est extrêmement moyennable, et que l'action canonique Aut(P)P est le flot minimal universel du groupe Aut(P) des homéomorphismes affines du simplexe de Poulsen P. Ceci répond aux questions de Melleray–Tsankov et Conley–Törnquist.

We show that the class of finite-dimensional Banach spaces and the class of finite-dimensional Choquet simplices have the Ramsey property. As an application, we show that the group Aut(G) of surjective linear isometries of the Gurarij space G is extremely amenable, and that the canonical action Aut(P)P is the universal minimal flow of the group Aut(P) of affine homeomorphisms of the Poulsen simplex P. This answers questions of Melleray–Tsankov and Conley–Törnquist.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2017.11.001

Dana Bartošová 1 ; Jordi Lopez-Abad 2 ; Martino Lupini 3 ; Brice Mbombo 4

1 Department of Mathematical Sciences, Carnegie Mellon University, PA, USA
2 Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, 28040 Madrid, Spain
3 Mathematics Department, California Institute of Technology, 1200 E. California Blvd, MC 253-37, Pasadena, CA 91125, USA
4 Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada
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     title = {The {Ramsey} property for {Banach} spaces and {Choquet} simplices, and applications},
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Dana Bartošová; Jordi Lopez-Abad; Martino Lupini; Brice Mbombo. The Ramsey property for Banach spaces and Choquet simplices, and applications. Comptes Rendus. Mathématique, Volume 355 (2017) no. 12, pp. 1242-1246. doi : 10.1016/j.crma.2017.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.11.001/

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