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

 

Invariant complementation and projectivity in the Fourier algebra


Author: Peter J. Wood
Journal: Proc. Amer. Math. Soc. 131 (2003), 1881-1890
MSC (2000): Primary 43A30; Secondary 46L07
Published electronically: November 4, 2002
MathSciNet review: 1955277
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Abstract: In this paper, we study the ideals in the Fourier algebra of a locally compact group $G$which are complemented by an invariant projection. In particular we show that when $G$ is discrete, every ideal which is complemented by a completely bounded projection must be invariantly complemented. Perhaps surprisingly, this result does not depend of the amenability of the group or the algebra, but instead relies on the operator biprojectivity of the Fourier algebra for a discrete group.


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Additional Information

Peter J. Wood
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: pwood@uwaterloo.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06742-4
PII: S 0002-9939(02)06742-4
Keywords: Fourier algebra, operator space, projective, complemented ideals
Received by editor(s): February 15, 2001
Received by editor(s) in revised form: February 8, 2002
Published electronically: November 4, 2002
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society