Journal of Operator Theory

Volume 32, Issue 2, Fall 1994 pp. 273-297.

Decomposition of completely positive maps

Authors: Ichiro Fujimoto
Author institution:Department of Mathematics, University of Florida, Gainesville, FL 32611, U.S.A.

Summary: We give a solution to the decomposition problem for completely positive maps by generalizing Choquet's theorem in the context of CP-convexity theory, i.e., if $A$ is a separable $C^*$-algebra and $H$ is a separable Hilbert space, then every CP-state $\psi \in Q_H (A)$ can be represented by a CP-measure $\lambda_\psi$ supported by the CP-extreme elements $D_h (A)$ of $Q_H (A)$.

Keywords: Completely positive maps, CP-convexity, Choquet's theorem.

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