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

@article{Bartovsova2017TheRP,
  title={The Ramsey property for Banach spaces and Choquet simplices, and applications},
  author={Dana Bartovsov'a and J. Lopez-Abad and M. Lupini and B. Mbombo},
  journal={Comptes Rendus Mathematique},
  year={2017},
  volume={355},
  pages={1242-1246}
}
  • Dana Bartovsov'a, J. Lopez-Abad, +1 author B. Mbombo
  • Published 2017
  • Mathematics
  • Comptes Rendus Mathematique
  • 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–Tornquist. 
    6 Citations

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