Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1976-0512370-0
MathSciNet review: 0512370
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de von Neumann), 2ième éd., Gauthier-Villars. Paris, 1969. MR 50 #5482. MR 0352996 (50:5482)
  • [2] F. J. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. (2) 44 (1943), 716-808. MR 5, 101. MR 0009096 (5:101a)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L10

Retrieve articles in all journals with MSC: 46L10


Additional Information

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

American Mathematical Society