ON TENSOR PRODUCTS OF INJECTIVE OPERATOR SPACES

We show that an infinite dimensional injective operator space V has an in finite dimensional operator subspace, completely isometric to the row or column Hilbert spaces or l(infinity). When the third case does not happen, we characterize V as a finite direct sum of bounded operators B (H, K) with H or K finite dimensional. We characterize injective operator spaces V and W for which the spacial (injective) tensor product V (sic) W is injective. We give a similar characterization for injectivity of the Haagerup tensor product of injective operator spaces.