Journal of the
Korean Mathematical Society JKMS

Let $\Bbb P_s$ be the convex cone of all $s$-positive linear maps from the matrix algebra $M_m(\Bbb C)$ into $M_n(\Bbb C)$. We show that every maximal face of $\Bbb P_s$ corresponds to an $m\times n$ matrix whose rank is less than or equal to $s$. We also discuss the relations between maximal faces of the cones $\Bbb P_s$ and $\Bbb P_t$ for different $s$ and $t$.

Keywords: Positive linear maps, matrix algebras, maximal faces

MSC numbers: 46L05, 15A30