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

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.

arXiv commentFinal version. 17 pages. Accepted for publication in Annales de l'Institut Fourier

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