Noncommutative function theory and unique extensions

David P. Blecher, and Louis E. Labuschagne. "Noncommutative function theory and unique extensions." Studia Mathematica 178.2 (2007): 177-195. <http://eudml.org/doc/285173>.

@article{DavidP2007,
abstract = {We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő $L^\{p\}$-distance estimate and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. As a byproduct, this completes the noncommutative analog of the famous cycle of theorems characterizing the function algebraic generalizations of $H^\{∞\}$ from the 1960’s. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and give a necessary condition for every completely contractive homomorphism on a unital subalgebra of a C*-algebra to have a unique completely positive extension.},
author = {David P. Blecher, Louis E. Labuschagne},
journal = {Studia Mathematica},
keywords = {subdiagonal operator algebra; noncommutative Hardy spaces; finite von Neumann algebras; unique extension; F. & M. Riesz theorem},
language = {eng},
number = {2},
pages = {177-195},
title = {Noncommutative function theory and unique extensions},
url = {http://eudml.org/doc/285173},
volume = {178},
year = {2007},
}

TY - JOUR
AU - David P. Blecher
AU - Louis E. Labuschagne
TI - Noncommutative function theory and unique extensions
JO - Studia Mathematica
PY - 2007
VL - 178
IS - 2
SP - 177
EP - 195
AB - We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő $L^{p}$-distance estimate and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. As a byproduct, this completes the noncommutative analog of the famous cycle of theorems characterizing the function algebraic generalizations of $H^{∞}$ from the 1960’s. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and give a necessary condition for every completely contractive homomorphism on a unital subalgebra of a C*-algebra to have a unique completely positive extension.
LA - eng
KW - subdiagonal operator algebra; noncommutative Hardy spaces; finite von Neumann algebras; unique extension; F. & M. Riesz theorem
UR - http://eudml.org/doc/285173
ER -