On noncommutative weak Orlicz-Hardy spaces

TL;DR

This paper introduces and studies noncommutative weak Orlicz spaces and their Hardy space variants, focusing on their properties and dual space characterizations within the framework of operator algebras.

Contribution

It is the first to define noncommutative weak Orlicz-Hardy spaces and analyze their duality properties, expanding the theory of noncommutative function spaces.

Findings

Defined noncommutative weak Orlicz spaces with weights

Characterized dual spaces of noncommutative weak Orlicz-Hardy spaces

Established foundational properties of these new spaces

Abstract

We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.