Some results on noncommutative Hardy-Lorentz spaces

Yazhou Han,Jingjing Shao

doi:10.1186/s13660-015-0642-3

Abstract

Let \(\mathcal{A}\) be a maximal subdiagonal algebra of a finite von Neumann algebra ℳ. For \(0< p<\infty\), we define the noncommutative Hardy-Lorentz spaces and establish the Riesz and Szegö factorizations on these spaces. We also present some results of Jordan morphism on these spaces.

Highlights

The concept of maximal subdiagonal algebras A, which appeared earlier in Arveson’s paper [ ], unifies analytic function spaces and nonselfadjoint operator algebras
Subdiagonal algebras are the noncommutative analogue of weak* Dirichlet algebras
The noncommutative Hp spaces have been developed by Blecher, Bekjan, Labuschagne, Xu and their coauthors in a series of papers

Summary

Introduction

The concept of maximal subdiagonal algebras A, which appeared earlier in Arveson’s paper [ ], unifies analytic function spaces and nonselfadjoint operator algebras. Let M have no minimal projection, the associate space a noncommutative Banach function space. Let M be a finite von Neumann algebra, we define noncommutative weighted Hardy spaces by Hp,ω(A) = [A]p,ω and H p,ω(A) = [A ]p,ω.

Results

Conclusion