Elsevier

Journal of Functional Analysis

Volume 272, Issue 3, 1 February 2017, Pages 976-1016
Journal of Functional Analysis

Johnson–Schechtman inequalities for noncommutative martingales

https://doi.org/10.1016/j.jfa.2016.11.002Get rights and content
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Abstract

In this paper we study Johnson–Schechtman inequalities for noncommutative martingales. More precisely, disjointification inequalities of noncommutative martingale difference sequences are proved in an arbitrary symmetric operator space E(M) of a finite von Neumann algebra M without making any assumption on the Boyd indices of E. We show that we can obtain Johnson–Schechtman inequalities for arbitrary martingale difference sequences and that, in contrast with the classical case of independent random variables or the noncommutative case of freely independent random variables, the inequalities are one-sided except when E=L2(0,1). As an application, we partly resolve a problem stated by Randrianantoanina and Wu in [46]. We also show that we can obtain sharp Φ-moment analogues for Orlicz functions satisfying p-convexity and q-concavity for 1p2, q=2 and p=2, 2<q<. This is new even for the classical case. We also extend and strengthen the noncommutative Burkholder–Gundy inequalities in symmetric spaces and in the Φ-moment case.

MSC

primary
46L52
46L53
47A30
secondary
60G42

Keywords

Noncommutative martingales
Johnson–Schechtman inequalities
Symmetric spaces
Φ-moment inequalities

Cited by (0)

1

Yong Jiao is supported by NSFC (11471337) and Natural Science Foundation of Hunan Province (14JJ1004).