Tensor products of the operator system generated by the Cuntz isometries (Q2835249)

Let \(\mathcal{O}_{n},\) \(S_{n}\)\ and \(S_{n}^{d}\) be respectively the Cuntz algebra, the operator system generated by the Cuntz isometries and the dual operator system of \(S_{n}\) (i.e., the operator system consisting of all bounded linear functionals on \(S_{n}\)). By using the nuclearity of the Cuntz algebra \(\mathcal{O}_{n}\), it is shown that \(S_{n}\) is \(C^{\ast}\)-nuclear, a fact that implies a dual row contraction version of Ando's theorem about operators of numerical radius 1. Section 4 is devoted to a nice proof of the nuclearity of \(\mathcal{O}_{n}.\) Another important result of this paper is Theorem 5.7 that asserts that the dual operator system of \(S_{n}^{d}\) is completely order isomorphic to an operator subsystem of \(M_{n+1}\). Finally, a lifting result concerning Popescu's joint numerical radius is proved via operator system techniques.