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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Best bounds for approximate identities in ideals of the Fourier algebra vanishing on subgroups


Authors: Brian Forrest and Nicolaas Spronk
Journal: Proc. Amer. Math. Soc. 134 (2006), 111-116
MSC (2000): Primary 43A30, 46J20; Secondary 46L07, 43A07
Published electronically: August 15, 2005
MathSciNet review: 2170550
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Abstract: In this paper we show that if $G$ is an amenable locally compact group and if $H$ is a closed subgroup, then the ideal $I(H)$ has an approximate identity of norm $2.$ If $H$ is not open, this bound is the best possible.


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Additional Information

Brian Forrest
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: beforres@math.uwaterloo.ca

Nicolaas Spronk
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: nspronk@uwaterloo.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08205-5
PII: S 0002-9939(05)08205-5
Keywords: Fourier algebra, ideal, bounded approximate identity, operator space
Received by editor(s): December 3, 2003
Published electronically: August 15, 2005
Additional Notes: The first author was supported in part by a grant from NSERC. The second author was a visiting assistant professor at Texas A&M University when this work was completed and was supported in part by an NSERC PDF
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.