Operator spaces with few completely bounded maps

We construct several examples of Hilbertian operator spaces with few completely bounded maps. In particular, we give an example of a separable 1-Hilbertian operator space X-0 such that, whenever X' is an infinite dimensional quotient of X-0, X is a subspace of X', and T:T : X --> X' is a completely bounded map, then T=lambdaI(X)+S, where S is compact Hilbert-Schmidt and ||S||(2)/16less than or equal to||S||(cb)less than or equal to||S||(2). Moreover, every infinite dimensional quotient of a subspace of X-0 fails the operator approximation property. We also show that every Banach space can be equipped with an operator space structure without the operator approximation property.