A Beurling-Blecher-Labuschagne theorem for Haagerup noncommutative $L^p$ spaces

Abstract

Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\phi$, and let $\mathcal{A}$ be maximal subdiagonal subalgebra of $\mathcal{M}$ and $1\le p<\8$. We prove a Beurling-Blecher-Labuschagne type theorem for $\mathcal{A}$-invariant subspaces of Haagerup noncommutative $L^p(\mathcal{M})$ and give a characterization of outer operators in Haagerup noncommutative $H^p$-spaces associated with $\mathcal{A}$.

16 pages

References in corpus (4)

• Riesz and Szegö type factorizations for noncommutative Hardy spaces
• A Beurling theorem for noncommutative L^p
• On the maximality of subdiagonal algebras
• A Beurling-Chen-Hadwin-Shen Theorem for Noncommutative Hardy Spaces Associated with Semifinite von Neumann Algebras with Unitarily Invariant Norms