Some inverse limits of Cuntz algebras

Abstract

We construct a nontrivial inverse system of Cuntz algebras $\{{\mathcal{O}}_n:2\le n<\infty \}$, whose inverse limit is *-isomorphic onto ${\mathcal{O}}_{\infty }$. By using this result, it is shown that the $K_0$-functor is discontinuous with respect to the inverse limit even if the limit is a C${}^{\ast }$-algebra.

24 pages

Cited by in corpus (1)

• Pure states on Cuntz algebras arising from geometric progressions