English

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

Group Theory 2024-03-25 v5 Functional Analysis Operator Algebras

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 L1L^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.

Keywords

Cite

@article{arxiv.2109.12949,
  title  = {Almost invariant CND kernels and proper uniformly Lipschitz actions on subspaces of $L^1$},
  author = {Ignacio Vergara},
  journal= {arXiv preprint arXiv:2109.12949},
  year   = {2024}
}

Comments

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