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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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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