Johnson-Schechtman and Khinchine inequalities in noncommutative probability theory

TL;DR

This paper extends Johnson-Schechtman and Khinchine inequalities to noncommutative probability, providing new bounds for noncommutative random variables in symmetric operator spaces and modulars.

Contribution

It introduces noncommutative versions of Johnson-Schechtman and Khinchine inequalities for independent variables in the sense of Junge and Xu.

Findings

Established noncommutative Johnson-Schechtman inequalities

Proved noncommutative Khinchine inequalities in symmetric operator spaces

Extended inequalities to modulars

Abstract

We prove disjointification inequalities due to Johnson and Schechtman for noncommutative random variables independent in the sense of Junge and Xu. In the same setting, we also prove noncommutative Khinchine inequalities. These inequalities are proved both for symmetric operator spaces and for modulars.