Proper metrics on locally compact groups, and proper affine isometric actions on Banach spaces

2006/06/30 by Uffe Haagerup, Haagerup, Uffe, Agata Przybyszewska +1 · 2 citations
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.math/0606794

arxiv created 2006/06/30 · openalex publication_date 2006/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article it is proved, that every locally compact second countable group has a left invariant metric d, which generates the topology on G, and which is proper, ie. every closed d-bounded set in G is compact. Moreover, we obtain the following extension of a result due to N. Brown and E. Guentner: Every locally compact second countable G admits a proper affine action on the reflexive and strictly convex Banach space \bigoplus^∞_n=1 L²ⁿ(G, dμ), where the direct sum is taken in the l²-sense.

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• Characterizing the Kirkwood-Dirac positivity on second countable LCA groups
• Permanence properties of property A and coarse embeddability for locally compact groups

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