Completely positive maps of the Cuntz algebras
The author constructs a covariant functor from the category whose objects are separable Hilbert spaces and whose morphisms are contractions, into the category whose objects are unital \(C^*\)-algebras and whose morphisms are completely positive, identity preserving maps. The \(C^*\)-algebras involved are isomorphic to the Cuntz algebra \({\mathcal O}_\infty\) and the functor extends the canonical action of the group of unitaries on the generating Hilbert space. For a related result see \textit{O. Bratteli}, \textit{D. E. Evans}, \textit{F. M. Goodman} and \textit{P. E. T. Jørgensen} [Publ. Res. Inst. Math. Sci. 22, 103-117 (1986; Zbl 0611.46064)].
scientific article; zbMATH DE number 1006667