The non-commutative Khintchine inequalities for p<1

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 Hölder on semifinite von Neumann algebras. The main tool is a new form of Hölder inequality for non commutative Lp spaces with weights.

arXiv commentMinor improvements (Remark 2.10 which was mistakenly omitted from previous version, is added to the current version). Paper will appear in J. Inst. Math Jussieu (unfortunately without Remark 2.10)