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

Author(s)

Bartosova, Dana ^[1] ; Lopez-Abad, Jordi ^[2] ; Lupini, Martino ^[3] ; Mbombo, Brice ^[4]

Affiliation

^[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 - USA

^[2] UNED, Fac Ciencias, Dept Matemat Fundamentales, Madrid 28040 - Spain

^[3] CALTECH, Math Dept, 1200 E Calif Blvd, MC 253-37, Pasadena, CA 91125 - USA

^[4] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5 - Canada

• Document type: Journal article
• Source: COMPTES RENDUS MATHEMATIQUE; v. 355, n. 12, p. 1242-1246, DEC 2017.
• Web of Science Citations: 0

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) curved right arrow 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. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved. (AU)

• FAPESP's process: 12/20084-1 - Universal topological groups
• Grantee: Brice Rodrigue Mbombo Dempowo
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/24827-1 - Ramsey theory methods in Banach spaces
• Grantee: Valentin Raphael Henri Ferenczi
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 13/14458-9 - Algebra in the Cech-Stone compactification and its applications to topological dynamics, ergodic theory and Ramsey theory.
• Grantee: Dana Bartosova
• Support Opportunities: Scholarships in Brazil - Post-Doctoral