Communicated by Abstract. We will prove that, if every finite dimensional subspace of an infinite dimensional operator space E is 1-completely complemented in it, E is 1-Hilbertian and 1-homogeneous. However, this is not true for finite dimensional operator spaces: we give an example of an n-dimensional operator space E, such that all of its subspaces are 1-completely complemented in E, but whi...