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Properties $ \Gamma $ and $ L$ for type $ {\rm II}\sb{1}$ factors


Author: Paul Willig
Journal: Proc. Amer. Math. Soc. 25 (1970), 836-837
MSC: Primary 46.65
DOI: https://doi.org/10.1090/S0002-9939-1970-0259630-3
MathSciNet review: 0259630
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Abstract: Using the new concept of central sequences introduced by Dixmier and Lance, it is proved that for a type $ {\operatorname{II} _1}$ factor on a separable Hilbert space properties $ \Gamma $ and $ L$ are equivalent.


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

  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Cahiers scientifiques, fasc. 25, Gauthier-Villars, Paris, 1957. MR 20 #1234. MR 0094722 (20:1234)
  • [2] -, Quelques propriétés des suites centrales dans les facteurs de type $ {\operatorname{II} _1}$, $ {\operatorname{II} _1}$, Invent Math. 7(1969), 215-225. MR 0248534 (40:1786)
  • [3] J. Dixmier and E. L. Lance, Deux nouveaux facteurs de type $ {\operatorname{II} _1}$, Invent. Math. 7 (1969), 226-234. MR 0248535 (40:1787)
  • [4] 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)
  • [5] L. Pukanszky, Some examples of factors, Publ. Math. Debrecen 4 (1956), 135-156. MR 18, 323 MR 0080894 (18:323a)

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DOI: https://doi.org/10.1090/S0002-9939-1970-0259630-3
Keywords: Factor, type $ {\operatorname{II} _1}$, property $ \Gamma $, property $ L$, central sequence
Article copyright: © Copyright 1970 American Mathematical Society

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