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arXiv:2307.00403 (math)
[Submitted on 1 Jul 2023 (v1), last revised 3 Sep 2024 (this version, v3)]

Title:Amenability of finite energy path and loop groups

Authors:Vladimir G. Pestov
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Abstract:It is shown that the groups of finite energy (that is, Sobolev class $H^1$) paths and loops with values in a compact Lie group are amenable in the sense of Pierre de la Harpe, that is, every continuous action of such a group on a compact space admits an invariant regular Borel probability measure. To our knowledge, the strongest previously known result concerned the amenability of groups of continuous paths and loops (Malliavin and Malliavin 1992).
Comments: LaTeX, 19 pp., the final version sent to the journal upon acceptance. A remark added at the end of Preliminaries with two new citations, a missing sign added in the proof of Lemma 3.6, minor grammatical inaccuracies fixed
Subjects: Functional Analysis (math.FA)
MSC classes: 22E67, 43A07
Cite as: arXiv:2307.00403 [math.FA]
  (or arXiv:2307.00403v3 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.2307.00403

Submission history

From: Vladimir Pestov [view email]
[v1] Sat, 1 Jul 2023 18:34:52 UTC (15 KB)
[v2] Wed, 1 May 2024 18:25:01 UTC (20 KB)
[v3] Tue, 3 Sep 2024 21:07:56 UTC (21 KB)
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