Properties $\Gamma$ and $L$ for type $\textrm {II}_{1}$ factors
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- by Paul Willig
- Proc. Amer. Math. Soc. 25 (1970), 836-837
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259630-3
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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
- Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722
- J. Dixmier, Quelques propriétés des suites centrales dans les facteurs de type $\textrm {II}_{1}$, Invent. Math. 7 (1969), 215–225 (French). MR 248534, DOI 10.1007/BF01404306
- J. Dixmier and E. C. Lance, Deux nouveaux facteurs de type $\textrm {II}_{1}$, Invent. Math. 7 (1969), 226–234 (French). MR 248535, DOI 10.1007/BF01404307
- 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
- L. Pukánszky, Some examples of factors, Publ. Math. Debrecen 4 (1956), 135–156. MR 80894, DOI 10.5486/pmd.1956.4.3-4.05
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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