Outers for noncommutative $H^{p}$ revisited
Volume 217 / 2013
Studia Mathematica 217 (2013), 265-287
MSC: Primary 46L51, 46L52, 46E15; Secondary 30H10, 46J15, 46K50.
DOI: 10.4064/sm217-3-4
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 $h a_n \in {\rm Ball}(A)$ and $h a_n \to 1$ in $p$-norm.
