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Operator biflatness of the Fourier algebra and approximate indicators for subgroups

Oleg Yu. Aristov·Volker Runde·Nico Spronk
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Abstract

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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Oleg Yu. Aristov, Volker Runde, Nico Spronk. 2003-04-10. Operator biflatness of the Fourier algebra and approximate indicators for subgroups. https://arxiv.org/abs/math/0203290

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