Outers for noncommutative Hp revisted

Abstract

We continue our study of outer elements of the noncommutative Hp spaces associated with Arveson's subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in Hp actually satisfy the stronger condition that there exist an∈A with han∈Ball(A) and han→1 in p-norm