Riesz and Szegö type factorizations for noncommutative Hardy spaces

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, 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 $p<1$.

To appear in J. Operator Theory

References in corpus (2)

• A Beurling theorem for noncommutative L^p
• Applications of the Fuglede-Kadison determinant: Szegö's theorem and outers for noncommutative $H^p$

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• Szegö's Theorem and its Probabilistic Descendants
• A Beurling-Chen-Hadwin-Shen Theorem for Noncommutative Hardy Spaces Associated with Semifinite von Neumann Algebras with Unitarily Invariant Norms
• A non-commutative Beurling's theorem with respect to unitarily invariant norms
• Interpolation of quasi noncommutative $L_p$-spaces
• Applications of the Fuglede-Kadison determinant: Szegö's theorem and outers for noncommutative $H^p$
• Complex interpolation of noncommutative Hardy spaces associated semifinite von Neumann algebra
• On pointwise products of symmetric quasi Banach spaces and applications
• A Helson-Szegö theorem for subdiagonal subalgebras with applications to Toeplitz operators
• A Beurling-Blecher-Labuschagne theorem for Haagerup noncommutative $L^p$ spaces