Tracial approximation in simple ${C}^{\ast }$ -algebras

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...

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Bibliographic Details
Published inCanadian journal of mathematics Vol. 74; no. 4; pp. 942 - 1004
Main Authors Fu, Xuanlong, Lin, Huaxin
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.08.2022
Cambridge University Press
Subjects
Algebra
Approximation
Asymptotic properties
Classification
Mathematical analysis
46L05
46L35
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0008-414X
1496-4279
DOI:10.4153/S0008414X21000158