Isometric embeddings of noncommutative Lp-spaces into noncommutative symmetric spaces

摘要: 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 7→ t−1/p, 0 < t ≤ 1, then there exists a noncommutative proba#2;
bility space (N , σ) such that Lp(M) is isometric to a subspace of E(N , σ). In
particular, this answers two questions raised by Randrianantoanina in 2006.