On the completely positive and positive-semidefinite-preserving cones (Q790207)

Let \(M_ n\), \(H_ n\), and \(P_ n\) be respectively the complex space of \(n\times n\) complex matrices, the real space of Hermitian matrices in \(M_ n\), and the cone of positive semidefinite matrices in \(H_ n\). The authors show that the cone \(CP_{n,q}\) of completely positive linear maps from \(M_ n\) to \(M_ q\) is isometrically isomorphic to the cone \(P_{nq}\), and identify certain right and left facial ideals in \(CP_{n,n}\). They define a joint angular field of values of a sequence \(K_ 1,...,K_ m\), \(K_ i\in H_ n\), and use it to characterize when a sum of dyad products \(\sum^{m}_{i=1}K_ i\otimes L_ i\), \(K_ i\in H_ n\), \(L_ i\in H_ q\), preserves semidefiniteness.