Extreme amenability of L₀, a Ramsey theorem, and Lévy groups

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• 作者：Ilijas Farah ; Sł ; awomir Solecki
• 关键词：Extremely amenable groups ; ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WJJ-4SGTM8T-2&_mathId=mml3&_user=1067359&_cdi=6880&_rdoc=5&_acct=C000050221&_version=1&_userid=10&md5=abe6524dca9
• 刊名：Journal of Functional Analysis
• 出版年：2008
• 出版时间：15 July 2008
• 年：2008
• 卷：255
• 期：2
• 页码：471-493
• 全文大小：242 K

文摘

We show that L₀(,H) is extremely amenable for any diffused submeasure and any solvable compact group H. This extends results of Herer–Christensen, and of Glasner and Furstenberg–Weiss. Proofs of these earlier results used spectral theory or concentration of measure. Our argument is based on a new Ramsey theorem proved using ideas coming from combinatorial applications of algebraic topological methods. Using this work, we give an example of a group which is extremely amenable and contains an increasing sequence of compact subgroups with dense union, but which does not contain a Lévy sequence of compact subgroups with dense union. This answers a question of Pestov. We also show that many Lévy groups have non-Lévy sequences, answering another question of Pestov.