Paulsen, Vern I.; Zheng, Da Tensor products of the operator system generated by the Cuntz isometries. (English) Zbl 1399.46082 J. Oper. Theory 76, No. 1, 67-91 (2016). 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. Reviewer: Mihai Pascu (Bucureşti) Cited in 1 Document MSC: 46L06 Tensor products of \(C^*\)-algebras 46L05 General theory of \(C^*\)-algebras 46L07 Operator spaces and completely bounded maps 47L25 Operator spaces (= matricially normed spaces) Keywords:Cuntz isometries; operator system tensor product; \(C^*\)-nuclearity; operator system quotient; dual row contraction; shorted operator; joint numerical radius PDFBibTeX XMLCite \textit{V. I. Paulsen} and \textit{D. Zheng}, J. Oper. Theory 76, No. 1, 67--91 (2016; Zbl 1399.46082) Full Text: DOI arXiv