Abstract
AbstractWe revisit the notion of tracial approximation for unital simple$C^*$-algebras. We show that a unital simple separable infinite dimensional$C^*$-algebraAis asymptotically tracially in the class of$C^*$-algebras with finite nuclear dimension if and only ifAis asymptotically tracially in the class of nuclear$\mathcal {Z}$-stable$C^*$-algebras.
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