arXiv math/06118332006-11math.OAmath.GR

$p$-Operator Spaces and Figá-Talamanca-Herz Algebras

Matthew Daws

备注：: LaTeX, 30 pages. Updated with minor corrections and added references
发表信息：: J. Operator Theory 63 (2010), no. 1, 47-83

英文摘要：

We study a generalisation of operator spaces modelled on $L_p$ spaces, instead of Hilbert spaces, using the notion of $p$-complete boundedness, as studied by Pisier and Le Merdy. We show that the Figá-Talamanca-Herz Algebras $A_p(G)$ becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact group $G$. We thus argue that we have presented a generalised of the use of operator spaces in studying the Fourier algebra $A(G)$, in the spirit of Ruan. Finally, we show that various notions of multipliers of $A_p(G)$ (including Herz's generalisation of the Fourier-Stieltjes algebra) naturally fit into this framework.

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