p-Operator Spaces and Figà-Talamanca-Herz Algebras

Abstract

We study a generalisation of operator spaces modelled on Lp spaces, instead of Hilbert spaces, using the notion of p-complete boundedness, as studied by Pisier and Le Merdy. We show that the Figà-Talamanca-Herz Algebras Ap(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 Ap(G) (including Herz’s generalisation of the Fourier-Stieltjes algebra) naturally fit into this framework. 2000 Mathematics Subject Classification: Primary 46J99; Secondary 22D12, 43A07, 43A15, 43A65, 46L07, 47L25

Cite this paper

@inproceedings{Daws2008pOperatorSA, title={p-Operator Spaces and Figà-Talamanca-Herz Algebras}, author={Matthew Daws}, year={2008} }