Almost invariant CND kernels and proper uniformly Lipschitz actions on subspaces of L¹

2021/09/27 by Vergara, Ignacio
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2109.12949

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 L¹ 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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