Abstract
A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra \( {\user1{\mathcal{A}}} \) is a tracial limit of CTracial limit, Tracial topological rank*-algebras in \( {\user1{\mathcal{I}}}^{{{\left( k \right)}}} \) if and only if \( {\user1{\mathcal{A}}} \) has tracial topological rank no more than k. We present several known results using the notion of tracial limits.
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*Supported by Shanghai Priority Academic Discipline and National Natural Science Foundation of China
**Supported by the Zhi-Jiang Professorship of East China Normal University. He is also supported by a grant from National Science Foundation of U. S.
***Supported by National Natural Science Foundation of China
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Hu*, S., Lin**, H. & Xue***, Y. Tracial Limit of C*-algebras. Acta Math Sinica 19, 535–556 (2003). https://doi.org/10.1007/s10114-003-0275-1
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DOI: https://doi.org/10.1007/s10114-003-0275-1