Operator biflatness of the Fourier algebra and approximate indicators for subgroups

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• 作者：Aristov ; Oleg Yu. ; Runde ; Volker ; Spronk ; Nico
• 关键词：22D25 (primary) ; 22E10 ; 43A30 ; 46L07 ; 46L89 ; 46M18 ; 47L25 ; 47L50 ; Locally compact groups ; Biflatness ; Fourier algebra ; (quantized) Banach homology ; Approximate indicator ; Kazhdan's property (T)
• 刊名：Journal of Functional Analysis
• 出版年：2004
• 出版时间：April 15, 2004
• 年：2004
• 卷：209
• 期：2
• 页码：367-387
• 全文大小：254 K

文摘

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 rôle 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×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×G fails to have an approximate indicator.