On Completely Positive Maps Defined by an Irreducible Correspondence
Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 434-441

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1990-071-2
Mots-clés : 46L10, 46L30
Anantharaman-Delaroche, C. On Completely Positive Maps Defined by an Irreducible Correspondence. Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 434-441. doi: 10.4153/CMB-1990-071-2
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[1] 1. C. Anantharaman-Delaroche, Havet, J. F., On approximate factorizations of completely positive maps, J. Funct. Anal. 90 (1990), 411–428. Google Scholar

[2] 2. Arveson, W. B., Subalgebras of C*-algebras, Acta Math. 123 (1969) 141–224. Google Scholar

[3] 3. Baillet, M., Denizeau, Y., Havet, J. F., Indice d'une espérance conditionnelle, Comp. Math. 66 (1988), 199–236. Google Scholar

[4] 4. Choi, M. D., Completely positive linear maps on complex matrices, Linear Alg. Appl. 10 (1975), 285– 290. Google Scholar

[5] 5. Connes, A., Jones, V., Property Tfor von Neumann algebras, Bull. London Math. Soc. 17 (1985), 57–62. Google Scholar

[6] 6. Dixmier, J., Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1969. Google Scholar

[7] 7. Haagerup, U., The standard form of von Neumann algebras, Math. Scand. 37 (1975), 271–283. Google Scholar

[8] 8. Mingo, J., The correspondence associated to an inner completely positive map, Math. Ann. 284 (1989) 121–135. Google Scholar

[9] 9. Paschke, W. L., Inner product modules over B*-algebras, Trans. Amer. Math. Soc. 182 (1973) 443–468. Google Scholar

[10] 10. Popa, S., Correspondences, Preprint. Google Scholar

[11] 11. Rieffel, M. A., Induced representations of C*-algebras, Advances in Math. 13 (1974) 176–257. Google Scholar

[12] 12. Rieffel, M. A., Morita equivalence for C*-algebras and W*-algebras, J. Pure Appl. Alg. 5 (1974), 51–96. Google Scholar

[13] 13. Takesaki, M., Theory of operator algebras I, Springer-Verlag, New-York, 1979. Google Scholar

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