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Published December 2017 | Submitted
Journal Article Open

The Ramsey property for Banach spaces and Choquet simplices, and applications

Abstract

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.

Additional Information

© 2017 Published by Elsevier Masson SAS on behalf of Académie des sciences. Received 11 August 2017, Accepted 6 November 2017, Available online 13 November 2017. Supported by the grant FAPESP2013/14458-9. Partially supported by the grant MTM 2012-31286 (Spain) and the FAPESP Grant 2013/24827-1 (Brazil). Partially supported by the NSF Grant DMS-1600186. Supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), processo 12/20084-1.

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August 19, 2023
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