Decomposable positive maps on 𝐶*-algebras

Abstract

It is shown that a positive linear map of a C ∗ {C^*} -algebra A A into B ( H ) B(H) is decomposable if and only if for all n ∈ N n \in {\mathbf {\textrm {N}}} whenever ( x i j ) ({x_{ij}}) and ( x j i ) ({x_{ji}}) belong to M n ( A ) + {M_n}{(A)^ + } then ( ϕ ( x i j ) ) (\phi ({x_{ij}})) belongs to M n ( B ( H ) ) + {M_n}{(B(H))^ + } .