UC Irvine

We define a family of Hilbertian operator spaces Hkn, 1 ≤ k ≤ n, containing the row and column Hilbert spaces Rn, Cn and show that an atomic subspace X ⊂ B(H) which is the range of a contractive projection on B(H) is isometrically completely contractive to an ℓ∞-sum of the Hkn and Cartan factors of types 1 to 4. We also give a classification up to complete isometry of w*-closed atomic JW*-triples which have no infinite-dimensional rank 1 w*-closed ideal. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.