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

Ignacio Vergara

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.

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 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.

Paper Structure

This paper contains 10 sections, 95 equations.

Table of Contents

  1. Introduction
  2. CND kernels and actions on $E\subseteq L^p$
  3. Kernels
  4. $L^p$ spaces
  5. Proof of Theorem \ref{['Thm_caract']}
  6. Groups acting on products of quasi-trees
  7. Quasi-isometries and the first proof
  8. The kernel $d_a$ and the second proof
  9. Weakly amenable groups
  10. A-TTT-menable groups

Theorems & Definitions (14)

  • proof
  • proof
  • proof
  • proof : Proof of Corollary \ref{['Cor_Lp']}
  • proof : First proof of Theorem \ref{['Thm_QT']}
  • proof
  • proof
  • proof
  • proof
  • proof
  • ...and 4 more