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September 10, 2025Open Access

Almost invariant CND kernels and proper uniformly Lipschitz actions on subspaces of L 1

Key Points

Groups satisfying the almost invariant condition are found to act properly on products of quasi-trees.
The study identifies weakly amenable groups with a Cowling–Haagerup constant of 1 as meeting this criterion.
Characterization also applies to a-TTT-menable groups, indicating broader implications for mathematical groups.
Conditionally negative definite kernels provide a framework for understanding group actions in topological spaces.

Abstract

We define the notion of almost invariant conditionally negative definite kernel and use it to give a characterisation of groups admitting a proper uniformly Lipschitz affine action on a subspace of an L 1 space. We show that this condition is satisfied by groups acting properly on products of quasi-trees, weakly amenable groups with Cowling–Haagerup constant 1, and a-TTT-menable groups.

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Cite This Study

I. Vergara (Fri,) studied this question.

synapsesocial.com/papers/68c1a76954b1d3bfb60e04dd https://doi.org/https://doi.org/10.5802/aif.3731