This is an announcement for the paper "The non-commutative Khintchine inequalities for $0<p<1$" by Gilles Pisier and Eric Ricard.
Abstract: We give a proof of the Khintchine inequalities in non-commutative $L_p$-spaces for all $0< p<1$. These new inequalities are valid for the Rademacher functions or Gaussian random variables, but also for more general sequences, e.g. for the analogues of such random variables in free probability. We also prove a factorization for operators from a Hilbert space to a non commutative $L_p$-space, which is new for $0<p<1$. We end by showing that Mazur maps are H"older on semifinite von Neumann algebras.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 2000 MSC 46L51, 46L07, 47L25, 47L20
Submitted from: pisier@math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.0222
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