Outers for noncommutative $H^p$ revisited

David P. Blecher, and Louis E. Labuschagne. "Outers for noncommutative $H^{p}$ revisited." Studia Mathematica 217.3 (2013): 265-287. <http://eudml.org/doc/285923>.

@article{DavidP2013,
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 aₙ ∈ A with haₙ ∈ Ball(A) and haₙ → 1 in p-norm.},
author = {David P. Blecher, Louis E. Labuschagne},
journal = {Studia Mathematica},
keywords = {subdiagonal operator algebra; noncommutative Hardy space; outer element; inner-outer factorization; finite von Neumann algebra},
language = {eng},
number = {3},
pages = {265-287},
title = {Outers for noncommutative $H^\{p\}$ revisited},
url = {http://eudml.org/doc/285923},
volume = {217},
year = {2013},
}

TY - JOUR
AU - David P. Blecher
AU - Louis E. Labuschagne
TI - Outers for noncommutative $H^{p}$ revisited
JO - Studia Mathematica
PY - 2013
VL - 217
IS - 3
SP - 265
EP - 287
AB - 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 aₙ ∈ A with haₙ ∈ Ball(A) and haₙ → 1 in p-norm.
LA - eng
KW - subdiagonal operator algebra; noncommutative Hardy space; outer element; inner-outer factorization; finite von Neumann algebra
UR - http://eudml.org/doc/285923
ER -