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Weak amenability of free products of hyperbolic and amenable groups

Part of: Abstract harmonic analysis Selfadjoint operator algebras Noncompact transformation groups Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  06 January 2022

Ignacio Vergara Open the ORCID record for Ignacio Vergara [Opens in a new window]
Ignacio Vergara*
Affiliation:
Leonhard Euler International Mathematical Institute, Saint-Petersburg State University, 14th Line 29B, Vasilyevsky Island, St. Petersburg, 199178, Russia. E-mail: [email protected]
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Abstract

We show that if G is an amenable group and H is a hyperbolic group, then the free product $G\ast H$ is weakly amenable. A key ingredient in the proof is the fact that $G\ast H$ is orbit equivalent to $\mathbb{Z}\ast H$ .

Keywords

Weak amenabilityfree productsorbit equivalence

MSC classification

Primary: 46L07: Operator spaces and completely bounded maps
Secondary: 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 43A07: Means on groups, semigroups, etc.; amenable groups 20F67: Hyperbolic groups and nonpositively curved groups 22F10: Measurable group actions
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 3 , September 2022 , pp. 698 - 701
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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