Noncommutative $L_p$-space and operator system

TL;DR

This paper demonstrates that noncommutative Lp-spaces fulfill the axioms of operator systems with a specific constant, enabling their embedding into bounded operators with controlled isomorphic and order-preserving properties.

Contribution

It establishes that noncommutative Lp-spaces can be viewed as operator systems with a precise dominating constant, linking them to the structure of B(H).

Findings

Noncommutative Lp-spaces satisfy operator system axioms with constant 2^{1/p}.

They can be embedded into B(H) with 2^{1/p}-complete isomorphism.

Embedding preserves complete order structure.

Abstract

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