Applications of the Fuglede-Kadison determinant: Szegö's theorem and outers for noncommutative $H^p$
| dc.creator | Blecher, David P. | |
| dc.creator | Labuschagne, Louis E. | |
| dc.date | 2006-09-25 | |
| dc.date | 2007-02-23 | |
| dc.date.accessioned | 2026-07-07T07:48:11Z | |
| dc.date.available | 2026-07-07T07:48:11Z | |
| dc.description | We first use properties of the Fuglede-Kadison determinant on $L^p(M)$, for a finite von Neumann algebra $M$, to give several useful variants of the noncommutative Szegö theorem for $L^p(M)$, including the one usually attributed to Kolmogorov and Krein. As an application, we solve the longstanding open problem concerning the noncommutative generalization, to Arveson's noncommutative $H^p$ spaces, of the famous `outer factorization' of functions $f$ with $\log |f|$ integrable. Using the Fuglede-Kadison determinant, we also generalize many other classical results concerning outer functions. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609662 | |
| dc.identifier | http://arxiv.org/abs/math/0609662 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124409 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 46L51, 46L52, 47L75 Secondary 30D55, 46J15, 46K50, 47L45 | |
| dc.title | Applications of the Fuglede-Kadison determinant: Szegö's theorem and outers for noncommutative $H^p$ | |
| dc.type | text |