Direct sums of operator spaces

It is proved that if X and Y are operator spaces such that every completely bounded operator from X into Y is completely compact and Z is a completely complemented subspace of X ⊕ Y, then there exists a completely bounded automorphism τ: X ⊕ Y → X ⊕ Y with completely bounded inverse such that τ Z = X₀ ⊕ Y₀, where X₀ and Y₀ are completely complemented subspaces of X and Y, respectively. If X and Y are homogeneous, the existence is proved of such a τ under a weaker assumption that any operator from X to Y is strictly singular. An upper estimate is obtained for ∥τ∥_cb∥τ^-1∥_cb if X and Y are separable homogeneous Hilbertian operator spaces. Also proved is the uniqueness of a 'completely unconditional' basis in X ⊕ Y if X and Y satisfy certain conditions.