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Proceedings of the American Mathematical Society

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The equivalence of various definitions for a properly infinite von Neumann algebra to be approximately finite dimensional


Authors: G. A. Elliott and E. J. Woods
Journal: Proc. Amer. Math. Soc. 60 (1976), 175-178
MSC: Primary 46L10
MathSciNet review: 0512370
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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 [Enhancements On Off] (What's this?)

  • [1] Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (algèbres de von Neumann), Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition, revue et augmentée; Cahiers Scientifiques, Fasc. XXV. MR 0352996
  • [2] F. J. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. (2) 44 (1943), 716–808. MR 0009096

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DOI: https://doi.org/10.1090/S0002-9939-1976-0512370-0
Article copyright: © Copyright 1976 American Mathematical Society