Duality for positive linear maps in matrix algebras

Abstract

We characterize extreme rays of the dual cone of the cone consisting of all s-positive (respectively t-copositive) linear maps between matrix algebras. This gives us a characterization of positive linear maps which are the sums of s-positive linear maps and t-copositive linear maps, which generalizes Størmer's characterization of decomposable positive linear maps in matrix algebras. With this duality, it is also easy to describe maximal faces of the cone consisting of all s-positive (respectively t-copositive) linear maps between matrix algebras.