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Indecomposable Positive Maps in Matrix Algebras

Published online by Cambridge University Press:  20 November 2018

Kôtarô Tanahashi  and
Jun Tomiyama
Kôtarô Tanahashi
Affiliation:
Department of Mathematics, Tohoku College of PharmacyKomatsushima, Sendai, 983, Japan
Jun Tomiyama
Affiliation:
Department of Mathematics, Tokyo Metropolitan UniversityFukasawa, Setagaya-Ku, Tokyo, 158, Japan
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Abstract

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We prove that Choi's map in M3 cannot be written as the sum of a 2-positive map and a 2-copositive map. We also provide other examples of positive maps in Mn which cannot be written as the sum of an n-positive map and a 2-copositive map.

Keywords

16A4215A30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 3 , 01 September 1988 , pp. 308 - 317
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Ando, T., Positivity of certain maps, seminar note 1985.Google Scholar
2. Choi, M. D., Positive linear maps on C*-algebras, Canad. J. Math. 24 (1972), pp. 520–529.Google Scholar
3. Choi, M. D., Positive semidefinite biquadratic forms, Linear Algebra and Appl. 12 (1975), pp. 95–100.Google Scholar
4. Choi, M. D., Some assorted inequalities for positive linear maps on C* -algebras, J. Operator Theory 4(1980), pp. 271–285.Google Scholar
5. Choi, M. D. and Lam, T. Y., Extremal positive semidefinite forms, Math. Ann. 231 (1977), pp. 1–18.Google Scholar
6. Lance, E. C., On nuclear C*-algebras, J. Funct. Analysis 12 (1973), pp. 157–176.Google Scholar
7. Robertson, A. G., Schwartz inequalities and decomposition of positive maps on C*-algebras, Math. Proc. Camb. Phil. Soc. 94 (1983), pp. 291–296.Google Scholar
8. Robertson, A. G., Positive projections on C*-algebras and an extremal positive map, J. London Math. Soc. 32(1985), pp. 133–140.Google Scholar
9. Størmer, E., Positive linear maps of operator algebras, Acta Math. 110 (1963), pp. 233–278.Google Scholar
10. Størmer, E., Decomposable positive maps on C*-algebras, Proc. Amer. Math. Soc. 86 (1982), pp. 402–404.Google Scholar
11. Tomiyama, J., On the transpose map of matrix algebras, Proc. Amer. Math. Soc. 88 (1983), pp. 635–638.Google Scholar
12. Tomiyama, J., On the geometry of positive maps in matrix algebras II, Linear Algebra and Appl. 69 (1985), pp. 169–177.Google Scholar
13. Tomiyama, J., On the geometry of positive maps in matrix algebras, Operator Algebras and Mathematical Physics, Contemp. Math. 62 (1985), pp. 357–364.Google Scholar
14. Woronowicz, S. L., Positive maps of low dimensional matrix algebras, Rep. Math. Phys. 10 (1976), pp. 165–183.Google Scholar