Journal of Operator Theory

Volume 62, Issue 1, Summer 2009 pp. 215-231.

Riesz and Szego type factorizations for noncommutative Hardy spaces

Authors: Turdebek N. Bekjan (1) and Quanhua Xu (2)
Author institution: (1) College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
(2) Laboratoire de Mathematiques, Universite de Franche-Comte, 25030 Besancon, cedex, France

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

Keywords: Subdiagonal algebras, noncommutative Hardy spaces, Riesz and Szegö factorizations, outer operators.

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