Nuclear dimension of extensions of ${\mathcal{O}}_{\infty }$-stable algebras

Abstract

We obtain an improved upper bound for the nuclear dimension of extensions of ${\mathcal{O}}_{\infty }$-stable ${\mathrm{C}}^{\ast }$-algebras. In particular, we prove that the nuclear dimension of a full extension of an ${\mathcal{O}}_{\infty }$-stable ${\mathrm{C}}^{\ast }$-algebra by a stable AF algebra is one.

17 pages; accepted version; J. Operator Theory, to appear