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In this paper we investigate operator Hilbert systems and their separablemorphisms. We prove that the operator Hilbert space of Pisier is an operatorsystem, which possesses the self-duality property. It is established a linkbetween unital positive maps and Pietch factorizations, which allows us todescribe all separable morphisms from an abelian C*-algebra to an operatorHilbert system. Finally, we prove a key property of entanglement breaking mapsthat involves operator Hilbert systems.

Separable morphisms of operator Hilbert systems, Pietsch factorizations and entanglement breaking maps