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Facial Structures for the Positive Linear Maps Between Matrix Algebras

Published online by Cambridge University Press:  20 November 2018

Seung-Hyeok Kye
Seung-Hyeok Kye*
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea, e-mail:kye@math.snu.ac.kr
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Abstract

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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 .

Keywords

46L0506B99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 74 - 82
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Choi, M.-D., Positive semidefinite biquadratic forms, Linear Algebra Appl. 12(1975), 95–100.Google Scholar
2. Choi, M.-D. and Lam, T.-T., Extremal positive semidefinite forms, Math. Ann. 231(1977), 1—18.Google Scholar
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. Kye, S.-H., Positive linear maps between matrix algebras which fix diagonals, Linear Algebra Appl. 216 (1995), 239–256.Google Scholar
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. Rockafellar, R. T., Convex Analysis, Princeton University Press (1970).Google Scholar
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. Stormer, E., Positive linear maps of operator algebras, Acta Math. 110(1963), 233—278.Google Scholar
9. Woronowicz, S. L., Positive maps of low dimensional matrix algebras, Rep. Math. Phys. 10( 1976), 165–183.Google Scholar