Ando, T. (2018). Positive map as difference of two completely positive or super-positive maps. Advances in Operator Theory, 3(1), 53-60. doi: 10.22034/aot.1702-1129

Tsuyoshi Ando. "Positive map as difference of two completely positive or super-positive maps". Advances in Operator Theory, 3, 1, 2018, 53-60. doi: 10.22034/aot.1702-1129

Ando, T. (2018). 'Positive map as difference of two completely positive or super-positive maps', Advances in Operator Theory, 3(1), pp. 53-60. doi: 10.22034/aot.1702-1129

Ando, T. Positive map as difference of two completely positive or super-positive maps. Advances in Operator Theory, 2018; 3(1): 53-60. doi: 10.22034/aot.1702-1129

Positive map as difference of two completely positive or super-positive maps

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.