Embeddings and $C^{\ast }$-envelopes of exact operator systems

Abstract

We prove a necessary and sufficient condition for embeddability of an operator system into ${\mathcal{O}}_2$. Using Kirchberg's theorems on a tensor product of ${\mathcal{O}}_2$ and ${\mathcal{O}}_{\infty }$, we establish results on their operator system counterparts ${\mathcal{S}}_2$ and ${\mathcal{S}}_{\infty }$. Applications of the results proved, including some examples describing $C^{\ast }$-envelopes of operator systems, are also discussed.

12 Pages. To appear in Bulletin of the Australian Mathematical Society

References in corpus (4)

• Operator space and operator system analogs of Kirchberg's nuclear embedding theorem
• The Operator System Generated by Cuntz Isometries
• A universal nuclear operator system
• Tensor Products of the Operator System Generated by the Cuntz Isometries

Cited by in corpus (1)

• Nuclearity properties and $C^{\ast }$-envelopes of operator system inductive limits