The equivalence of various definitions for a properly infinite von Neumann algebra to be approximately finite dimensional
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- by G. A. Elliott and E. J. Woods PDF
- Proc. Amer. Math. Soc. 60 (1976), 175-178 Request permission
Abstract:
If a properly infinite von Neumann algebra on a separable Hilbert space is approximately finite dimensional with respect to the $\ast$-ultrastrong topology, that is, if any finite number of elements may be approximated $\ast$-ultrastrongly by elements of a finite-dimensional sub $\ast$-algebra, then the algebra may be expressed as the bicommutant of an increasing sequence of factors of type ${{\text {I}}_{{2^n}}}$.References
- Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition, revue et augmentée. MR 0352996
- F. J. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. (2) 44 (1943), 716–808. MR 9096, DOI 10.2307/1969107
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 175-178
- MSC: Primary 46L10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0512370-0
- MathSciNet review: 0512370