A noncommutative Davis' decomposition for martingales

TL;DR

This paper extends Davis' decomposition to noncommutative martingales in L_p-spaces, characterizes the dual of noncommutative conditioned Hardy spaces, and broadens results to 1<p<2.

Contribution

It introduces a noncommutative version of Davis' decomposition involving square functions and identifies the dual space of noncommutative conditioned Hardy spaces.

Findings

Established a noncommutative Davis' decomposition for martingales.

Determined the dual space of noncommutative conditioned Hardy space \h_1.

Extended duality results to the range 1<p<2.

Abstract

We prove an analogue of the classical Davis' decomposition for martingales in noncommutative L_p-spaces, involving the square functions. We also determine the dual space of the noncommutative conditioned Hardy space \h_1. We further extend this latter result to the case 1<p<2.