Embeddings of non-commutative L_p-spaces into non-commutative L₁-spaces, 1 < p < 2

It will be shown that for < p < 2 the Schatten p-class is isometrically isomorphic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative L_p(N, τ)-spaces defined by a finite trace on a finite von Neumann algebra. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting.