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On the completely positive and positive-semidefinite-preserving cones. (English) Zbl 0534.15012
Let M n , H n , and P n be respectively the complex space of n×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 H n , and use it to characterize when a sum of dyad products i=1 m K i L i , K i H n , L i H q , preserves semidefiniteness.
Reviewer: D.Carlson

15A48Positive matrices and their generalizations (MSC2000)
06F20Ordered abelian groups, etc.