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.

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

References in corpus (3)

• Property (QT) for 3-manifold groups
• Hyperbolicity and uniformly Lipschitz affine actions on subspaces of $L^1$
• Property (T) for uniformly bounded representations and weak*-continuity of invariant means