Skip to main content
Log in

Facial structures for positive linear maps in two-dimensional matrix algebra

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

We completely determine the lattice structure for the faces of the convex cone of all positive linear maps between the 2×2 matrix algebras, in terms of pairs of subspaces of M 2.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cho, S.-J., Kye, S.-H. and Lee, S.G.: Generalized Choi maps in 3-dimensional matrix algebras, Linear Alg. Appl. 171: 213-224, 1992.

    Google Scholar 

  2. Choi,M.-D.: Completely positive linear maps on complex matrices, Linear Alg. Appl. 10: 285-290, 1975.

    Google Scholar 

  3. Choi, M.-D.: Positive semidefinite biquadratic forms, Linear Alg. Appl. 12: 95-100.

  4. Choi,M.-D. and Lam, T.-T.: Extremal positive semidefinite forms, Math. Ann. 231: 1-18, 1977.

    Google Scholar 

  5. Eom, M.-H. and Kye, S.-H.: Duality for positive linear maps in matrix algebras, Math. Scand. 86: 130-142, 2000.

    Google Scholar 

  6. Ha, K.-C.: Atomic positive linear maps in matrix algebras, RIMS, Kyoto Univ., 34: 591-599, 1998.

    Google Scholar 

  7. Kim, H.-J. and Kye, S.-H.: Indecomposable extreme positive linear maps in matrix algebras, Bull. London Math. Soc. 26: 575-581, 1994.

    Google Scholar 

  8. Kraus, K.: Operations and effects in the Hilbert space formulation of quantum theory, Foundations and quantum mechanics and ordered linear spaces (Marburg, 1973), pp. 206-229. Lecture Notes in Phys., Vol. 29, Springer, 1974.

    Google Scholar 

  9. Kye, S.-H.: A class of atomic positive maps in 3-dimensional matrix algebras, Elementary operators and applications (Blaubeuren, 1991), pp. 205-209, World-Scientific, 1992.

  10. Kye, S.-H.: Facial structures for positive linear maps between matrix algebras, Can. Math. Bull. 39: 74-82, 1996.

    Google Scholar 

  11. Kye, S.-H.: Boundaries of the cone of positive linear maps and its subcones in matrix algebras, Math. Proc. Cambridge Philos. Soc. 122: 45-54, 1997.

    Google Scholar 

  12. Kye, S.-H.: On the convex set of all completely positive linear maps in matrix algebras, Math. Proc. Cambridge Philos. Soc. 122: 45-54, 1997.

    Google Scholar 

  13. Kye, S.-H.: Facial structures for decomposable positive linear maps in matrix algebras, preprint.

  14. Osaka, H.: A class of extremal positive maps in 3×3 matrix algebras, RIMS, kyoto Univ. 28: 747-756, 1992.

    Google Scholar 

  15. Robertson, A.G.: Positive projections on C*-algebras and extremal positive maps, J. London Math. Soc. (2) 32: 133-140, 1985.

    Google Scholar 

  16. Størmer, E.: Positive linear maps of operator algebras Acta Math. 110: 233-278, 1963.

    Google Scholar 

  17. Størmer, E.: Decomposable positive maps on C*-algebras, Proc. Amer. Math. Soc. 86: 402-404, 1982.

    Google Scholar 

  18. Tanahashi, K. and Tomiyama, J.: Indecomposable positive maps in matrix algebras, Can. Math. Bull. 31: 308-317, 1988.

    Google Scholar 

  19. Woronowicz, S.L.: Positive maps of low dimensional matrix algebras, Rep. Math. Phys. 10: 165-183, 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Byeon, ES., Kye, SH. Facial structures for positive linear maps in two-dimensional matrix algebra. Positivity 6, 369–380 (2002). https://doi.org/10.1023/A:1021397312586

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021397312586

Keywords

Navigation