Subdiagonal algebras with Beurling type invariant subspaces

Abstract

Let A be a maximal subdiagonal algebra in a σ-finite von Neumann algebra M. If every right invariant subspace of A in the noncommutative Hardy space H2 is of Beurling type, then we say A is of type 1. We determine generators of these algebras and consider a Riesz type factorization theorem for the noncommutative H1 space. We show that the right analytic Toeplitz algebra on the noncommutative Hardy space Hp associated with a type 1 subdiagonal algebra with multiplicity 1 is hereditary reflexive.