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

DOI:
https://doi.org/10.1090/S0002-9939-02-06742-4

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 which are complemented by an invariant projection. In particular we show that when 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:
https://doi.org/10.1090/S0002-9939-02-06742-4

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