Facial Structures for the Positive Linear Maps Between Matrix Algebras
Canadian mathematical bulletin, Tome 39 (1996) no. 1, pp. 74-82

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

Let denote the convex set of all positive linear maps from the matrix algebra Mn (C) into itself. We construct a join homomorphism from the complete lattice of all faces of into the complete lattice of all join homomorphisms between the lattice of all subspaces of Cn . We also characterize all maximal faces of .
DOI : 10.4153/CMB-1996-010-x
Mots-clés : 46L05, 06B99
Kye, Seung-Hyeok. Facial Structures for the Positive Linear Maps Between Matrix Algebras. Canadian mathematical bulletin, Tome 39 (1996) no. 1, pp. 74-82. doi: 10.4153/CMB-1996-010-x
@article{10_4153_CMB_1996_010_x,
     author = {Kye, Seung-Hyeok},
     title = {Facial {Structures} for the {Positive} {Linear} {Maps} {Between} {Matrix} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {74--82},
     year = {1996},
     volume = {39},
     number = {1},
     doi = {10.4153/CMB-1996-010-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-010-x/}
}
TY  - JOUR
AU  - Kye, Seung-Hyeok
TI  - Facial Structures for the Positive Linear Maps Between Matrix Algebras
JO  - Canadian mathematical bulletin
PY  - 1996
SP  - 74
EP  - 82
VL  - 39
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-010-x/
DO  - 10.4153/CMB-1996-010-x
ID  - 10_4153_CMB_1996_010_x
ER  - 
%0 Journal Article
%A Kye, Seung-Hyeok
%T Facial Structures for the Positive Linear Maps Between Matrix Algebras
%J Canadian mathematical bulletin
%D 1996
%P 74-82
%V 39
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-010-x/
%R 10.4153/CMB-1996-010-x
%F 10_4153_CMB_1996_010_x

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

[2] 2. Choi, M.-D. and Lam, T.-T., Extremal positive semidefinite forms, Math. Ann. 231(1977), 1—18. Google Scholar

[3] 3. Kim, H.-J. and Kye, S.-H., Indecomposable extreme positive linear maps in matrix algebras, Bull. London Math. Soc. 26(1994), 575–581. Google Scholar

[4] 4. Kye, S.-H., Positive linear maps between matrix algebras which fix diagonals, Linear Algebra Appl. 216 (1995), 239–256. Google Scholar

[5] 5. Robertson, A. G., Positive projections on C* -algebras and extremal positive maps, J. London Math. Soc. (2)32(1985), 133–140. Google Scholar

[6] 6. Rockafellar, R. T., Convex Analysis, Princeton University Press (1970). Google Scholar

[7] 7. Smith, R. R. and Ward, J. D., The geometric structure of generalized state spaces, J. Funct. Anal. 40(1981), 170–184. Google Scholar

[8] 8. Stormer, E., Positive linear maps of operator algebras, Acta Math. 110(1963), 233—278. Google Scholar

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

Cité par Sources :