Properties $\Gamma$ and $L$ for type $\textrm {II}_{1}$ 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 | References | Similar Articles | Additional Information
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.
- 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 ${\rm II}_{1}$, Invent. Math. 7 (1969), 215–225 (French). MR 248534, DOI https://doi.org/10.1007/BF01404306
- J. Dixmier and E. C. Lance, Deux nouveaux facteurs de type ${\rm II}_{1}$, Invent. Math. 7 (1969), 226–234 (French). MR 248535, DOI https://doi.org/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 https://doi.org/10.2307/1969107
- L. Pukánszky, Some examples of factors, Publ. Math. Debrecen 4 (1956), 135–156. MR 80894
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Additional Information
Keywords:
Factor,
type <!– MATH ${\operatorname {II} _1}$ –> <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\operatorname {II} _1}$">,
property <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$\Gamma$">,
property <IMG WIDTH="19" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img12.gif" ALT="$L$">,
central sequence
Article copyright:
© Copyright 1970
American Mathematical Society