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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An example of a weight with type III centralizer


Author: Uffe Haagerup
Journal: Proc. Amer. Math. Soc. 62 (1977), 278-280
MSC: Primary 46L10
MathSciNet review: 0430801
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an example of a weight $ \phi $ on the hyperfinite type $ {\text{II}_\infty }$ factor R, such that the centralizer $ {M_\phi }$ of $ \phi $ is a type III von Neumann algebra.


References [Enhancements On Off] (What's this?)

  • [1] François Combes, Poids et espérances conditionnelles dans les algèbres de von Neumann, Bull. Soc. Math. France 99 (1971), 73–112 (French). MR 0288589 (44 #5785)
  • [2] F. Combes and C. Delaroche, Groupe modulaire d'une espérance conditionnelle dans une algèbre de von Neumann, Université d'Orléans, 1974 (preprint).
  • [3] A. Connes and M. Takesake, Flow of weights on factors of type III, 1975 (preprint).
  • [4] Gert K. Pedersen and Masamichi Takesaki, The Radon-Nikodym theorem for von Neumann algebras, Acta Math. 130 (1973), 53–87. MR 0412827 (54 #948)
  • [5] Shôichirô Sakai, $ {C^\ast}$-algebras and $ {W^\ast}$-algebras, Springer-Verlag, Berlin, 1971.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0430801-2
PII: S 0002-9939(1977)0430801-2
Keywords: von Neumann algebras, Tomita-Takesaki theory, weights
Article copyright: © Copyright 1977 American Mathematical Society