Tracial approximation in simple C*-algebras

2020/04/22 by Xuanlong Fu, Fu, Xuanlong, Huaxin Lin +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2004.10901

openalex publication_date 2020/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable 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 simple nuclear Z-stable C*-algebras.

Related

• some properties for asymptotically tracially approximation of C*-algebras
• Comparison properties of asymptotically tracially approximation C*-algebras
• Certain properties of generalized tracially approximated C*-algebras
• Generalized Tracially Approximated C*-algebras
• Non-unital tracially approximated \rm C^*-algebras