Noncommutative $L_p$-space and operator system

Abstract

We show that noncommutative $L_p$-spaces satisfy the axioms of the (nonunital) operator system with a dominating constant $2^{\frac{1}{p}}$. Therefore, noncommutative $L_p$-spaces can be embedded into $B(H)$ $2^{\frac{1}{p}}$-completely isomorphically and complete order isomorphically.

10 pages, final version, to appear in PAMS