Divisible properties for asymptotically tracially approximation ${\mathrm{C}}^{\ast }$-algebras

Abstract

We show that the following divisible properties of the ${\mathrm{C}}^{\ast }$-algebras in a class $\mathcal{P}$ are inherited by simple unital ${\mathrm{C}}^{\ast }$-algebras in the class of asymptotically tracially in $\mathcal{P}$: $(1)$ $m$-almost divisible, $(2)$ weakly $(m,n)$-divisible.