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The Fourier Algebra for Locally Compact Groupoids

Published online by Cambridge University Press:  20 November 2018

Alan L. T. Paterson
Alan L. T. Paterson*
Affiliation:
Department of Mathematics, University of Mississippi, University, MS 38677, U.S.A. e-mail: mmap@olemiss.edu
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Abstract

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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.

Keywords

43A32Fourier algebralocally compact groupoidsHilbert modulespositive definite functionscompletely bounded maps
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 6 , 01 December 2004 , pp. 1259 - 1289
Copyright
Copyright © Canadian Mathematical Society 2004

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