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Some C*-algebras properties preserved by tracial approximation

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Abstract

We show that the Riesz interpolation property of the K 0-monoid of C*-algebras in the class Ω is inherited by simple unital C*-algebras in the class TAΩ, and the property of being an admissible target algebras of finite type in the class of Ω is inherited by unital C*-algebras in the class TAΩ.

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References

  1. M. Dadarlat and S. Eilers, On the classification of nuclear C*-algebras, Proceedings London Mathematical Society 85 (2002), 168–210.

    MathSciNet  MATH  Google Scholar 

  2. G. A. Elliott, On the classification of the inductive limts of sequences of semisimple finite dimensional algebras, Journal of Algebra 38 (1976), 29–44.

    Article  MathSciNet  MATH  Google Scholar 

  3. G. A. Elliott and Z. Niu, On tracial approximation, Journal of Functional Analysis 254 (2008), 396–440.

    Article  MathSciNet  MATH  Google Scholar 

  4. Q. Fan and X. Fang, Non-simple tracial approximation, Houston Journal of Mathematics 37 (2011), 1249–1263.

    MathSciNet  MATH  Google Scholar 

  5. S. Hu, H. Lin and Y. Xue, The tracial topological rank of C*-algebras (II), Mathematica Scandinavica 94 (2004), 125–147.

    MathSciNet  MATH  Google Scholar 

  6. S. Hu, H. Lin and Y. Xue, K-theory of C*-algebras with tracial topological rank k, International Journal of Mathematics 14 (2003), 153–170.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Lin, The tracial topological rank of C*-algebras, Proceedings London Mathematical Society 83 (2001), 199–234.

    Article  MATH  Google Scholar 

  8. H. Lin, An Introduction to the Classification of Amenable C*-algebras, World Scientific, New Jersey, London, Singapore, Hong Kong, 2001.

    Book  MATH  Google Scholar 

  9. Z. Niu, A classification of certain tracially approximately subhomogeneous C*-algebras, PhD thesis, University of Toronto, 2005.

  10. H. Yao and S. Hu, C*-algebras of tracial real rank zero, Journal of East China Normal University, Natural Science Edition, 2 (2004), 5–12.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Maritime University, 1550 Haigang Ave, New Harbor City, Shanghai, 201306, China

    Qingzhai Fan

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  1. Qingzhai Fan
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Correspondence to Qingzhai Fan.

Additional information

Supported by the National Natural Science Foundation of China Grant No. (11101268 and 11071159) and supported by Innovation Program of Shanghai Municipal Education Commission No. (13YZ088).

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Fan, Q. Some C*-algebras properties preserved by tracial approximation. Isr. J. Math. 195, 545–563 (2013). https://doi.org/10.1007/s11856-012-0157-2

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  • DOI: https://doi.org/10.1007/s11856-012-0157-2

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