Duality for symmetric Hardy spaces of noncommutative martingales

TL;DR

This paper characterizes the dual spaces of certain noncommutative Hardy spaces and explores their relationships, advancing the understanding of noncommutative martingale theory.

Contribution

It provides a detailed description of dual spaces and links between symmetric and conditioned Hardy spaces in the noncommutative setting.

Findings

Dual spaces of conditional and symmetric Hardy spaces are explicitly characterized.

Relationships between symmetric Hardy spaces and their conditioned versions are established.

The results deepen the theoretical framework of noncommutative martingale Hardy spaces.

Abstract

We show the dual spaces of conditional Hardy space and symmetric Hardy space of noncommutative martingales. We derive relationship between the symmetric Hardy space of noncommutative martingales and its conditioned version.