Noncommutative function theory and unique extensions
| dc.creator | Blecher, David P. | |
| dc.creator | Labuschagne, Louis E. | |
| dc.date | 2006-03-17 | |
| dc.date.accessioned | 2026-07-07T07:07:02Z | |
| dc.date.available | 2026-07-07T07:07:02Z | |
| dc.description | We generalize to the setting of Arveson's maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegö $L^p$-distance estimate, and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. In so doing, we are finally able to provide a complete noncommutative analog of the famous cycle of theorems characterizing the function theoretic generalizations of $H^\infty$. 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 when every completely contractive homomorphism on a unital subalgebra of a C*-algebra possesses a unique completely positive extension. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603437 | |
| dc.identifier | http://arxiv.org/abs/math/0603437 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110243 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 46L51, 46L52, 47A15, Secondary 46J15, 46K50, 47L45 | |
| dc.title | Noncommutative function theory and unique extensions | |
| dc.type | text |