Isometric embeddings of noncommutative Lp-spaces into noncommutative symmetric spaces

Abstract: We establish a noncommutative version of a familiar Johnson–Maurey–Schechtman–Tzafriri Theorem, by showing that for any 0 < p < 2 and a (not necessarily semifinite) von Neumann algebra M on a separable Hilbert space, if a symmetric quasi-Banach function space E(0, 1) containing the function t → t^{−1/p}, 0 < t ≤ 1, then there exists a noncommutative proba#2;
bility space (N , σ) such that L_p(M) is isometric to a subspace of E(N , σ). In particular, this answers two questions raised by Randrianantoanina in 2006.