2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124409We 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.16 pagesOperator AlgebrasFunctional AnalysisPrimary 46L51, 46L52, 47L75 Secondary 30D55, 46J15, 46K50, 47L45text