Weak Amenability of Hyperbolic Groups

2007/04/12 by Narutaka Ozawa, Ozawa, Narutaka · 3 citations
Mathematics · #20F67 #43A65 #46L07 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.0704.1635

openalex publication_date 2007/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• Multipliers of the Fourier Algebras of Some Simple Lie Groups and Their Discrete Subgroups

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