On Riesz type factorization for noncommutative Hardy spaces

Abstract

We extended the Riesz type weak factorization to symmetric quasi Hardy spaces associated with semifinite subdiagonal algebras and the Haagerup noncommutative \(H^{p}\)-spaces under certain conditions. We also proved weak version of the Szego type factorization for symmetric quasi Hardy spaces associated with semifinite subdiagonal algebras and the Haagerup noncommutative \(H^{p}\)-spaces associated with subdiagonal algebras, which have the universal factorization property.