Rosenthal's theorem for subspaces of noncommutative L_p

We show that a reflexive subspace of the predual of a von Neumann algebra embeds into a noncommutative L_p-spacefor some p > 1. This is a noncommutative version of Rosenthal's result for commutative L _p-spaces. Similarly for 1 ≤ q < 2, an infinite-dimensional subspace X of a noncommutative L_q-space either contains ℓ_q or embeds in L_p for some q < p < 2. The novelty in the noncommutative setting is a double-sided change of density.