Abstract
For a linear map from ${\mathbb M}_m$ to ${\mathbb M}_n$, besides the usual positivity, there are two stronger notions, complete positivity and super positivity. Given a positive linear map $\varphi$ we study a decomposition $\varphi = \varphi^{(1)} - \varphi^{(2)}$ with completely positive linear maps $\varphi^{(j)} (j = 1,2)$. Here $\varphi^{(1)} + \varphi^{(2)}$ is of simple form with norm small as possible. The same problem is discussed with super-positivity in place of complete positivity.
Citation
Tsuyoshi Ando. "Positive map as difference of two completely positive or super-positive maps." Adv. Oper. Theory 3 (1) 53 - 60, Winter 2018. https://doi.org/10.22034/aot.1702-1129
Information