Outers for noncommutative $H^{p}$ revisited

Volume 217 / 2013

David P. Blecher, Louis E. Labuschagne 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.

Authors

  • David P. BlecherDepartment of Mathematics
    University of Houston
    Houston, TX 77204-3008, U.S.A.
    e-mail
  • Louis E. LabuschagneInternal Box 209
    School of Computer,
    Statistical and Mathematical Sciences
    North-West University
    Pvt. Bag X6001
    2520 Potchefstroom, South Africa
    e-mail

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