A non-commutative version of Nikishin's theorem

Abstract

© 2014 Royal Dutch Mathematical Society (KWG). 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).