Subdiagonal algebras with the Beurling type invariant subspaces

Abstract

Let $\mathfrak{A}$ be a maximal subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal{M}$. If every right invariant subspace of $\mathfrak{A}$ in the non-commutative Hardy space $H^2$ is of Beurling type, then we say $\mathfrak{A}$ to be type 1. We determine generators of these algebras and consider a Riesz type factorization theorem for the non-commutative $H^1$ space. We show that the right analytic Toeplitz algebra on the non-commutative Hardy space $H^p$ associated with a type 1 subdiagonal algebra with multiplicity 1 is hereditary reflexive.

17 pages

References in corpus (2)

• A Beurling theorem for noncommutative L^p
• On the maximality of subdiagonal algebras