This is an announcement for the paper "Operator space Lp embedding theory I" by Marius Junge and Javier Parcet.

Abstract: Given any $1 < q \le 2$, we use new free probability techniques to construct a completely isomorphic embedding of $\ell_q$ (equipped with its natural operator space structure) into the predual of a sufficiently large QWEP von Neumann algebra.

Archive classification: math.OA math.PR

Mathematics Subject Classification: 46L07; 46L51; 46L52; 46L54

Remarks: This is the most accessible part of our paper Operator space embedding of Lq into Lp, 28 pages.

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http://front.math.ucdavis.edu/0706.0550

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http://arXiv.org/abs/0706.0550

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