A completely positive map associated with a positive map

Details A completely positive map associated with a positive map A completely positive map associated with a positive map

2010-09-29

arxiv.org/abs/1009.5809v1

Mathematics

Operator Algebras

Scientific paper

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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