Geodesic
The Asymptotic Ratio Set and Direct Integral Decompositions of a Von Neumann Algebra
Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 598-607

Voir la notice de l'article provenant de la source Cambridge University Press

The fact that any von Neumann algebra on a separable Hilbert space has an essentially unique direct integral decomposition into factors means that there is a global as well as a local aspect to any partial classification of von Neumann algebras. More precisely, suppose that J is a statement about von Neumann algebras which is either true or false for any given von Neumann algebra. Then a von Neumann algebra is said to satisfy J globally if it satisfies J, and to satsify J locally if almost all the factors appearing in some (and hence in any) central decomposition of it satisfy J . In a recent paper [3], H. Araki and E. J. Woods introduced the notion of the asymptotic ratio set of a factor, and by means of this they made remarkable progress in the classification of factors. 
Nielsen, Ole A. The Asymptotic Ratio Set and Direct Integral Decompositions of a Von Neumann Algebra. Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 598-607. doi: 10.4153/CJM-1971-067-4
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