Applications of the Fuglede-Kadison determinant: Szegö’s theorem and outers for noncommutative $H^p$
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- by David P. Blecher and Louis E. Labuschagne PDF
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Abstract:
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.References
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Additional Information
- David P. Blecher
- Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3008
- Email: dblecher@math.uh.edu
- Louis E. Labuschagne
- Affiliation: Department of Mathematical Sciences, P.O. Box 392, 0003 UNISA, South Africa
- MR Author ID: 254377
- Email: labusle@unisa.ac.za
- Received by editor(s): September 20, 2006
- Received by editor(s) in revised form: February 22, 2007
- Published electronically: June 26, 2008
- Additional Notes: The first author was partially supported by grant DMS 0400731 from the National Science Foundation
The second author was partially supported by a National Research Foundation Focus Area Grant - © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 6131-6147
- MSC (2000): Primary 46L51, 46L52, 47L75; Secondary 46J15, 46K50, 47L45
- DOI: https://doi.org/10.1090/S0002-9947-08-04506-6
- MathSciNet review: 2425707