A non-commutative version of Nikishin’s theorem - Tikhonov, O.E.; Veselova, L.V. (Indagationes mathematicae, 2015)
Let τ be a tracial normal state on a von Neumann algebra, L1(τ) be the space of integrable self-adjoint operators, and S be the space of self-adjoint measurable operators. We prove that every positive linear operator from an ordered Banach space to S can be factorized through L1(τ).