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arXiv · 1009.5809

A completely positive map associated with a positive map

Erling Størmer
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Abstract

We show that each positive map from B(K) to B(H) with K and H finite dimensional Hilbert spaces is a scalar multiple of a map of the form $Tr - \psi$ with $\psi$ completely positive. This is used to give necessary and sufficient conditions for maps to be C-positive for a large class of mapping cones; in particular we apply the results to k-positive maps.

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Erling Størmer. 2010-09-29. A completely positive map associated with a positive map. https://arxiv.org/abs/1009.5809

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