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On Completely Positive Maps Defined by an Irreducible Correspondence

Published online by Cambridge University Press:  20 November 2018

C. Anantharaman-Delaroche
C. Anantharaman-Delaroche*
Affiliation:
Université d'Orléans Département de Mathématiques et d'Informatique B.P. 6759, 45067 ORLEANS Cedex 2, France
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Abstract

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Completely positive maps defined by an irreducible correspondence between two von Neumann algebras M and N are introduced. We give results about their structure and characterize, among them, those which are extreme points in the convex set of all unital completely positive maps from M to N. As particular cases we obtain known results of M. D. Choi [4] on completely positive maps between complex matrices and of J. A. Mingo [8] on inner completely positive maps.

Keywords

46L1046L30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 434 - 441
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. C. Anantharaman-Delaroche, Havet, J. F., On approximate factorizations of completely positive maps, J. Funct. Anal. 90 (1990), 411–428.Google Scholar
2. Arveson, W. B., Subalgebras of C*-algebras, Acta Math. 123 (1969) 141–224.Google Scholar
3. Baillet, M., Denizeau, Y., Havet, J. F., Indice d'une espérance conditionnelle, Comp. Math. 66 (1988), 199–236.Google Scholar
4. Choi, M. D., Completely positive linear maps on complex matrices, Linear Alg. Appl. 10 (1975), 285– 290.Google Scholar
5. Connes, A., Jones, V., Property Tfor von Neumann algebras, Bull. London Math. Soc. 17 (1985), 57–62.Google Scholar
6. Dixmier, J., Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1969.Google Scholar
7. Haagerup, U., The standard form of von Neumann algebras, Math. Scand. 37 (1975), 271–283.Google Scholar
8. Mingo, J., The correspondence associated to an inner completely positive map, Math. Ann. 284 (1989) 121–135.Google Scholar
9. Paschke, W. L., Inner product modules over B*-algebras, Trans. Amer. Math. Soc. 182 (1973) 443–468.Google Scholar
10. Popa, S., Correspondences, Preprint.Google Scholar
11. Rieffel, M. A., Induced representations of C*-algebras, Advances in Math. 13 (1974) 176–257.Google Scholar
12. Rieffel, M. A., Morita equivalence for C*-algebras and W*-algebras, J. Pure Appl. Alg. 5 (1974), 51–96.Google Scholar
13. Takesaki, M., Theory of operator algebras I, Springer-Verlag, New-York, 1979.Google Scholar