The Fourier algebra for locally compact groupoids

2003/10/08 by Alan L. T. Paterson, Paterson, Alan L. T. · 1 citation
Mathematics · #43A32 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.FA #math.OA #msc:43A32

paper · pdf · doi:10.48550/arxiv.math/0310115

31 pages

arxiv created 2003/10/08 · openalex publication_date 2003/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.

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• Weak containment of representation on topological groupoids

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