Weak Amenability of Hyperbolic Groups

Abstract

We prove that hyperbolic groups are weakly amenable. This partially extends the result of Cowling and Haagerup showing that lattices in simple Lie groups of real rank one are weakly amenable. We take a combinatorial approach in the spirit of Haagerup and prove that for the word length metric d on a hyperbolic group, the Schur multipliers associated with r^d have uniformly bounded norms for 0<r<1. We then combine this with a Bozejko-Picardello type inequality to obtain weak amenability.

8 pages. Final version. Groups Geom. Dyn., to appear

References in corpus (1)

• Weak amenability of CAT(0) cubical groups

Cited by in corpus (2)

• An l^{p}-Version of von Neumann Dimension for Representations of Equivalence Relations
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