Outers for noncommutative H^p revisited

TL;DR

This paper advances the theory of outer elements in noncommutative H^p spaces, extending factorization theorems and characterizations to include elements with zero determinant, enriching the understanding of outers.

Contribution

It generalizes the inner-outer factorization and characterization of outer elements to the zero determinant case in noncommutative H^p spaces.

Findings

Extended the generalized inner-outer factorization theorem.

Characterized outer elements with zero determinant.

Connected outers to stronger approximation conditions.

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.