대한수학회지 (Journal of the Korean Mathematical Society)
- 제33권3호
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- Pages.669-677
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
BOUNDARIES OF THE CONE OF POSITIVE LINEAR MAPS AND ITS SUBCONES IN MATRIX ALGEBRAS
초록
Let $M_n$ be the $C^*$-algebra of all $n \times n$ matrices over the complex field, and $P[M_m, M_n]$ the convex cone of all positive linear maps from $M_m$ into $M_n$ that is, the maps which send the set of positive semidefinite matrices in $M_m$ into the set of positive semi-definite matrices in $M_n$. The convex structures of $P[M_m, M_n]$ are highly complicated even in low dimensions, and several authors [CL, KK, LW, O, R, S, W]have considered the possibility of decomposition of $P[M_m, M_n] into subcones.