Subdiagonal algebras with Beurling type invariant subspaces

Let U be a maximal subdiagonal algebra in a sigma-finite von Neumann algebra M. If every right invariant subspace of U in the noncommutative Hardy space H-2 is of Beurling type, then we say U is of type 1. We determine generators of these algebras and consider a Riesz type factorization theorem for the noncommutative H-1 space. We show that the right analytic Toeplitz algebra on the noncommutative Hardy space H-P associated with a type 1 subdiagonal algebra with multiplicity 1 is hereditary reflexive. (C) 2019 Elsevier Inc. All rights reserved.