Semigroup algebra in the Stone-Cech compactification of a discrete semigroup
Christian Rosendal | University of Illinois at Chicago - United States
| Full text | |
| Author(s): |
Ferenczi, V
;
Lopez-Abad, J.
;
Mbombo, B.
;
Todorcevic, S.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | ADVANCES IN MATHEMATICS; v. 369, p. 76-pg., 2020-08-05. |
| Abstract | |
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) | |
| FAPESP's process: | 16/25574-8 - Geometry of Banach Spaces |
| Grantee: | Valentin Raphael Henri Ferenczi |
| Support Opportunities: | Research Projects - Thematic Grants |
| 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: | 13/11390-4 - Twisted sums, positions and Ramsey theory in Banach Spaces |
| Grantee: | Valentin Raphael Henri Ferenczi |
| Support Opportunities: | Regular Research Grants |