Geodesic
Indecomposable Positive Maps in Matrix Algebras
Canadian mathematical bulletin, Tome 31 (1988) no. 3, pp. 308-317

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

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.
DOI : 10.4153/CMB-1988-044-4
Mots-clés : 16A42, 15A30 
Tanahashi, Kôtarô; Tomiyama, Jun. Indecomposable Positive Maps in Matrix Algebras. Canadian mathematical bulletin, Tome 31 (1988) no. 3, pp. 308-317. doi: 10.4153/CMB-1988-044-4
@article{10_4153_CMB_1988_044_4,
     author = {Tanahashi, K\^otar\^o and Tomiyama, Jun},
     title = {Indecomposable {Positive} {Maps} in {Matrix} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {308--317},
     year = {1988},
     volume = {31},
     number = {3},
     doi = {10.4153/CMB-1988-044-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-044-4/}
}
TY  - JOUR
AU  - Tanahashi, Kôtarô
AU  - Tomiyama, Jun
TI  - Indecomposable Positive Maps in Matrix Algebras
JO  - Canadian mathematical bulletin
PY  - 1988
SP  - 308
EP  - 317
VL  - 31
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-044-4/
DO  - 10.4153/CMB-1988-044-4
ID  - 10_4153_CMB_1988_044_4
ER  - 
%0 Journal Article
%A Tanahashi, Kôtarô
%A Tomiyama, Jun
%T Indecomposable Positive Maps in Matrix Algebras
%J Canadian mathematical bulletin
%D 1988
%P 308-317
%V 31
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-044-4/
%R 10.4153/CMB-1988-044-4
%F 10_4153_CMB_1988_044_4

[1] 1. Ando, T., Positivity of certain maps, seminar note 1985. Google Scholar

[2] 2. Choi, M. D., Positive linear maps on C*-algebras, Canad. J. Math. 24 (1972), pp. 520–529. Google Scholar

[3] 3. Choi, M. D., Positive semidefinite biquadratic forms, Linear Algebra and Appl. 12 (1975), pp. 95–100. Google Scholar

[4] 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] 5. Choi, M. D. and Lam, T. Y., Extremal positive semidefinite forms, Math. Ann. 231 (1977), pp. 1–18. Google Scholar

[6] 6. Lance, E. C., On nuclear C*-algebras, J. Funct. Analysis 12 (1973), pp. 157–176. Google Scholar

[7] 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] 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] 9. Størmer, E., Positive linear maps of operator algebras, Acta Math. 110 (1963), pp. 233–278. Google Scholar

[10] 10. Størmer, E., Decomposable positive maps on C*-algebras, Proc. Amer. Math. Soc. 86 (1982), pp. 402–404. Google Scholar

[11] 11. Tomiyama, J., On the transpose map of matrix algebras, Proc. Amer. Math. Soc. 88 (1983), pp. 635–638. Google Scholar

[12] 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] 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] 14. Woronowicz, S. L., Positive maps of low dimensional matrix algebras, Rep. Math. Phys. 10 (1976), pp. 165–183. Google Scholar

Cité par Sources :