Characterizing Schwarz maps by tracial inequalities

Eric A. Carlen, Alexander Müller-Hermes

Let $\varphi$ be a linear map from the $n\times n$ matrices ${\mathcal{M}}_n$ to the $m\times m$ matrices ${\mathcal{M}}_m$. It is known that $\varphi$ is $2$-positive if and only if for all $K\…