Geodesic
Tracial approximation in simple ${C}^{\ast }$-algebras
Canadian journal of mathematics, Tome 74 (2022) no. 4, pp. 942-1004

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DOI

We revisit the notion of tracial approximation for unital simple $C^*$-algebras. We show that a unital simple separable infinite dimensional $C^*$-algebra A is asymptotically tracially in the class of $C^*$-algebras with finite nuclear dimension if and only if A is asymptotically tracially in the class of nuclear $\mathcal {Z}$-stable $C^*$-algebras. 
Fu, Xuanlong; Lin, Huaxin. Tracial approximation in simple ${C}^{\ast }$-algebras. Canadian journal of mathematics, Tome 74 (2022) no. 4, pp. 942-1004. doi: 10.4153/S0008414X21000158
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     author = {Fu, Xuanlong and Lin, Huaxin},
     title = {Tracial approximation in simple ${C}^{\ast }$-algebras},
     journal = {Canadian journal of mathematics},
     pages = {942--1004},
     year = {2022},
     volume = {74},
     number = {4},
     doi = {10.4153/S0008414X21000158},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000158/}
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