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THE NON-COMMUTATIVE KHINTCHINE INEQUALITIES FOR $0<p<1$

Part of: Selfadjoint operator algebras Linear spaces and algebras of operators

Published online by Cambridge University Press:  14 October 2015

Gilles Pisier  and
Éric Ricard
Gilles Pisier
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA ([email protected])
Éric Ricard
Affiliation:
Laboratoire de Mathématiques Nicolas Oresme, Université de Caen Normandie, BP 5186, F 14032, Caen, France ([email protected])
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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, for example, 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.

Keywords

Non-commutative Lp -spacesKhintchine inequalities

MSC classification

Primary: 46L51: Noncommutative measure and integration 46L07: Operator spaces and completely bounded maps 47L25: Operator spaces (= matricially normed spaces) 47L20: Operator ideals
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 5 , November 2017 , pp. 1103 - 1123
Copyright
© Cambridge University Press 2015 

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