Invariant complementation and projectivity in the Fourier algebra

Wood, Peter

doi:10.1090/S0002-9939-02-06742-4

Invariant complementation and projectivity in the Fourier algebra
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by Peter J. Wood PDF

Proc. Amer. Math. Soc. 131 (2003), 1881-1890 Request permission

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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