The complete isomorphism class of an operator space

Abstract

Abstract. Suppose X is an infinite-dimensional operator space and n is a positive integer. We prove that for every C > 0 there exists an operator spacẽ X such that the formal identity map id : X →X is a complete isomorphism, I M n ⊗id is an isometry, and d cb (X,X) > C. This provides a non-commutative counterpart to a recent result of W. Johnson and E. Odell.