On the generators of separable unital C*-algebras

Abstract

Let $A$ be a separable unital ${\mathrm{C}}^{\ast }$-algebra with nonempty tracial state space and strict comparison by ordinary tracial states. If $\mathcal{Z}$ embeds unitally into $A$, then $A$ is singly generated. In particular, every simple separable unital ${\mathrm{C}}^{\ast }$-algebra $A$ with $\mathrm{T}(A)\ne \varnothing$ and strict comparison is singly generated.

arXiv comment60 pages. The trace condition of the early version is completely removed. Any simple unital separable C*-algebra with strict comparison is shown to be singly generated