Divisible properties for asymptotically tracially approximation ${\rm C^*}$-algebras

TL;DR

This paper investigates how certain divisible properties of C*-algebras are preserved when passing to simple unital C*-algebras that are asymptotically tracially approximated by a class of C*-algebras.

Contribution

It establishes that specific divisible properties are inherited by simple unital C*-algebras in the asymptotic tracial approximation class.

Findings

Divisible properties like m-almost divisible are inherited.

Weakly (m, n)-divisible properties are preserved.

Results apply to a broad class of asymptotically tracially approximated C*-algebras.

Abstract

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