Reflexivity of a finite dimensional subspaces of operators

Abstract. We show that any n-dimensional subspace of B(H) is [ 2n]-reflexive, where [t] denotes the largest integer that is less than or equal to t ∈ R. As a corollary, we prove that if ϕ is an elementary operator on a C∗-algebra A with minimal length l, then ϕ is completely positive if and only if ϕ is max{[p2(l − 1)], 1}-positive