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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 1, pp 97–110 | Cite as

Some Properties of Tracially Quasidiagonal Extensions

  • Yile Zhao
  • Xiaochun FangEmail author
  • Xiaoming Xu
Article
  • 8 Downloads

Abstract

Suppose that 0 → IAA/I → 0 is a tracially quasidiagonal extension of C* -algebras. In this paper, the authors give two descriptions of the K0, K1 index maps which are induced by the above extension and show that for any ϵ > 0, any τ in the tracial state space of A/I and any projection \(\bar p \in A/I\) (any unitary \(\bar u \in A/I\), there exists a projection pA (a unitary uA) such that \(|\tau (\bar p) = \tau (\pi (p))| < \in (|\tau (\bar u) = \tau (\pi (u))| < \in )\).

Keywords

Tracially topological rank Quasidiagonal extension Tracially quasidiagonal extension 

2000 MR Subject Classification

46L05 46L35 

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsHangzhou Normal UniversityHangzhouChina
  2. 2.Department of MathematicsTongji UniversityShanghaiChina
  3. 3.School of ScienceShanghai Institute of TechnologyShanghaiChina

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