Explicit necessary and sufficient conditions are given for positivity, complete positivity, and k-positivity of diagonal perturbations of Tomiyama maps on matrix algebras of arbitrary size.
Choi, Completely positive linear maps on complex matrices,Linear Algebra Appl
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Tomiyama-type maps with a diagonal perturbation
Explicit necessary and sufficient conditions are given for positivity, complete positivity, and k-positivity of diagonal perturbations of Tomiyama maps on matrix algebras of arbitrary size.