On the geometry of positive maps in matrix algebras. II

Geometric relations among the identity map, the transpose map, and the map $\text{τ(x)?}\text{1}\text{n}\text{(x)}\text{Tr}\text{(x)1}{}_{\mathrm{n}}$ in the matrix algebra M_n are illustrated, providing parametric examples of maps which are not k+1-positive but which satisfy the matrix Schwartz inequality of order k for 1 ? k ? n ? 1.