Certain properties of generalized tracially approximated C*-algebras

Abstract

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

arXiv comment18 pages. arXiv admin note: text overlap with arXiv:2203.05700