Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-20T18:30:59.931Z Has data issue: false hasContentIssue false
  • English
  • Français

On Approximately Finite-Dimensional Von Neuman Algebras, II

Published online by Cambridge University Press:  20 November 2018

George A. Elliott
George A. Elliott*
Affiliation:
Department of Mathematics, University of Ottawa, Ottawa, Ont., Canada K1N 6N5
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An intrinsic characterization is given of those von Neumann algebras which are injective objects in the category of C*-algebras with completely positive maps. For countably generated von Neumann algebras several such characterizations have been given, so it is in fact enough to observe that an injective von Neumann algebra is generated by an upward directed collection of injective countably generated sub von Neumann algebras. The present work also shows that three of the intrinsic characterizations known in the countably generated case hold in general.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 415 - 418
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Connes, A., On hyperfinite factors of type III0 and Krieger's factors, J. Functional Analysis 18 (1975), 318-327.Google Scholar
2. Connes, A., Classification of injective factors, Ann. of Math. 104 (1976), 73-115.Google Scholar
3. Connes, A., On the cohomology of operator algebras, J. Functional Analysis 28 (1978), 248-253.Google Scholar
4. Elliott, G. A., On approximately finite-dimensional von Neumann algebras, Math. Scand. 39 (1976), 91-101.Google Scholar
5. Elliott, G. A. and Woods, E. J., The equivalence of various definitions for a properly infinite von Neumann algebra to be approximately finite-dimensional, Proc. Amer. Math. Soc. 60 (1976), 175-178.Google Scholar
6. Takesaki, M., Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math. 131 (1973), 249-310.Google Scholar
7. Tomiyama, J., Tensor products and projections of norm one in von Neumann algebras, lecture notes, University of Copenhagen, 1970.Google Scholar
8. Willig, P., On hyperfinite W*-algebras, Proc. Amer. Math. Soc. 40 (1973), 120-122.Google Scholar