Amalgamation and Ramsey properties of L-p spaces

Autor(es)

Ferenczi, V ; Lopez-Abad, J. ; Mbombo, B. ; Todorcevic, S.

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN MATHEMATICS; v. 369, p. 76-pg., 2020-08-05.

Resumo

We study the dynamics of the group of isometries of L-p-spaces. In particular, we study the canonical actions of these groups on the space of delta-isometric embeddings of finite dimensional subspaces of L-p(0, 1) into itself, and we show that for every real number 1 <= p < infinity with p not equal 4, 6, 8,... they are epsilon-transitive provided that delta is small enough. We achieve this by extending the classical equimeasurability principle of Plotkin and Rudin. We define the central notion of a Fraisse Banach space which underlies these results and of which the known separable examples are the spaces L-p(0, 1), p not equal 4, 6, 8,... and the Gurarij space. We also give a proof of Ramsey property of the classes {l(p)(n)}(n), p not equal 2, infinity, viewing it as a multidimensional Borsuk-Ulam statement. We relate this to an arithmetic version of the Dual Ramsey Theorem of Graham and Rothschild as well as to the notion of a spreading vector of Matousek and Rodl. Finally, we give a version of the Kechris-Pestov-Todorcevic correspondence that links the dynamics of the group of isometries of an approximately ultrahomogeneous space X with a Ramsey property of the collection of finite dimensional subspaces of X. Crown Copyright (C) 2020 Published by Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 16/25574-8 - Geometria dos espaços de Banach
• Beneficiário: Valentin Raphael Henri Ferenczi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/20084-1 - Grupos topológicos universais
• Beneficiário: Brice Rodrigue Mbombo Dempowo
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 13/24827-1 - Métodos de teoria de Ramsey em espaços de Banach
• Beneficiário: Valentin Raphael Henri Ferenczi
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 13/11390-4 - Somas torcidas, posições, e Teoria de Ramsey em Espaços de Banach
• Beneficiário: Valentin Raphael Henri Ferenczi
• Modalidade de apoio: Auxílio à Pesquisa - Regular