Certain properties of generalized tracially approximated C*-algebras

Abstract

We show that the following properties of unital ${\rm C^*}$-algebra in a class of $\Omega$ are preserved by unital simple ${\rm C^*}$-algebra in the class of $\rm WTA\Omega$: $(1)$ uniform property $\Gamma$, $(2)$ a certain type of tracial nuclear dimension at most $n$, $(3)$ weakly $(m, n)$-divisible.