Riesz and Szeg\"o type factorizations for noncommutative Hardy spaces

TL;DR

This paper extends key factorization results like Riesz and Szeg"o for noncommutative Hardy spaces associated with finite subdiagonal algebras, introducing new tools such as the contractivity of conditional expectations for all positive indices.

Contribution

It generalizes existing factorization theorems to all positive p in noncommutative Hardy spaces and introduces the contractivity of conditional expectations for p<1.

Findings

Extended Riesz, Szeg"o, and inner-outer factorizations to all positive p

Proved contractivity of conditional expectation on H^p for p<1

Unified framework for noncommutative Hardy space factorizations

Abstract

Let $\A$ be a finite subdiagonal algebra in Arveson's sense. Let $H^p(\A)$ be the associated noncommutative Hardy spaces, $0<p\le\8$. We extend to the case of all positive indices most recent results about these spaces, which include notably the Riesz, Szeg\"o and inner-outer type factorizations. One new tool of the paper is the contractivity of the underlying conditional expectation on $H^p(\A)$ for $p<1$.