Operator biflatness of the Fourier algebra and approximate indicators for subgroups

Details Operator biflatness of the Fourier algebra and approximate indicators for subgroups Operator biflatness of the Fourier algebra and approximate indicators for subgroups

2002-03-28

arxiv.org/abs/math/0203290v7

J. Funct. Anal. 209 (2004), 367-387

Mathematics

Functional Analysis

23 pages; more typos removed; references updated

Scientific paper

We investigate if, for a locally compact group $G$, the Fourier algebra $A(G)$ is biflat in the sense of quantized Banach homology. A central role in our investigation is played by the notion of an approximate indicator of a closed subgroup of $G$: The Fourier algebra is operator biflat whenever the diagonal in $G \times G$ has an approximate indicator. Although we have been unable to settle the question of whether $A(G)$ is always operator biflat, we show that, for $G = SL(3,C)$, the diagonal in $G \times G$ fails to have an approximate indicator.

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