We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő -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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-2-4,
author = {David P. Blecher and Louis E. Labuschagne},
title = {Noncommutative function theory and unique extensions},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {177-195},
zbl = {1121.46048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-2-4}
}
David P. Blecher; Louis E. Labuschagne. Noncommutative function theory and unique extensions. Studia Mathematica, Tome 178 (2007) pp. 177-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-2-4/