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.
Kye, Compositions and Tensor Products of Linear Maps between Matrix Algebras, Linear Algebra Appl.654, 1 (2022)
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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.