Outers for noncommutative H^p revisited

Abstract

We continue our study of outer elements of the noncommutative H^p 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 H^p actually satisfy the stronger condition that there exist a_n in A with h a_n in Ball(A) and h a_n \to 1 in p-norm.