Applications of the Fuglede-Kadison determinant: Szegö’s theorem and outers for noncommutative ^{}

By D. Blecher, L. Labuschagne. 2006

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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 Szego 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.

Subfields: Applied Mathematics, Mathematical Physics

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