The Operator System Generated by Cuntz Isometries

In this paper we consider the operator system $\text{cl}{S}_n$ generated by $n$ Cuntz isometries, i.e. the span of the generators of the Cuntz algebra $\text{cl}{O}_n$ together with their adjoints and the identity. We define an operator subsystem $\text{cl}{E}_n\subseteq M_{n+1}$ and then prove that $\text{cl}{S}_n$ is completely order isomorphic to a quotient of $\text{cl}{E}_n$. This result implies a characterization of positive elements in $M_p(\text{cl}{S}_n)$.