Tensor Products of the Operator System Generated by the Cuntz Isometries

2015/07/24 by Vern I. Paulsen, Paulsen, Vern I., Da Wei Zheng +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1507.06958

openalex publication_date 2015/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study tensor products and nuclearity-related properties of the operator system \mathcal S_n generated by the Cuntz isometries. By using the nuclearity of the Cuntz algebra, we can show that S_n is C^*-nuclear, and this implies a dual row contraction version of Ando's theorem characterizing operators of numerical radius 1. On the other hand, without using the nuclearity of the Cuntz algebra, we are still able to show directly this Ando type property of dual row contractions and conclude that S_n is C^*-nuclear, which yields a new proof of the nuclearity of the Cuntz algebras. We prove that the dual operator system of S_n 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.

Cited by

• Products and factorization in operator systems

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• Quotients, exactness, and nuclearity in the operator system category
• The Operator System Generated by Cuntz Isometries
• Nuclearity Related Properties in Operator Systems
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• On simplicity of Cuntz algebra and its generalizations