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On the convex set of completely positive linear maps in matrix algebras

Published online by Cambridge University Press:  01 July 1997

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

Let PI (respectively CPI) be the convex compact set of all unital positive (respectively completely positive) linear maps from the matrix algebra Mm([Copf ]) into Mn([Copf ]). We show that maximal faces of CPI correspond to one dimensional subspaces of the vector space Mm, n([Copf ]). Furthermore, a maximal face of CPI lies on the boundary of PI if and only if the corresponding subspace is generated by a rank one matrix.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 1 , July 1997 , pp. 45 - 54
Copyright
Cambridge Philosophical Society 1997

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