Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Weakly amenable groups and amalgamated products

Authors: Marek Bożejko and Massimo A. Picardello
Journal: Proc. Amer. Math. Soc. 117 (1993), 1039-1046
MSC: Primary 43A22; Secondary 20E06, 20E08, 43A07, 46J99
MathSciNet review: 1119263
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Abstract: Denote by $ {B_2}(G)$ the Herz-Schur multiplier algebra of a locally compact group $ G$ and by $ {B_{2,\lambda }}(G)$ the closure of the Fourier algebra in the topology of pointwise convergence boundedly in the norm of $ {B_2}(G)$. $ G$ is said to be weakly amenable if $ {B_{2,\lambda }}(G) = {B_2}(G)$. We show that every amalgamated product of a countable collection of locally compact amenable groups over a compact open subgroup is weakly amenable. This improves and extends previous results that hold for amalgams of compact groups.

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Keywords: Herz-Schur multipliers, weakly amenable groups, topological groups with amalgamation, homogeneous and semihomogeneous trees, positive definite functions
Article copyright: © Copyright 1993 American Mathematical Society