Strict comparison and $$ \mathcal{Z} $$ -absorption of nuclear$C$^{∗}-algebras

Hiroki Matui Graduate School of Science, Chiba University Yasuhiko Sato Graduate School of Science, Kyoto University

Quantum Algebra Rings and Algebras Spectral Theory and Operator Algebra mathscidoc:1701.29003

Acta Mathematica, 209, (1), 179-196, 2011.11
For any unital separable simple infinite-dimensional nuclear$C$^{∗}-algebra with finitely many extremal traces, we prove that $$ \mathcal{Z} $$ -absorption, strict comparison and property (SI) are equivalent. We also show that any unital separable simple nuclear$C$^{∗}-algebra with tracial rank zero is approximately divisible, and hence is $$ \mathcal{Z} $$ -absorbing.
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@inproceedings{hiroki2011strict,
  title={Strict comparison and $$ \mathcal{Z} $$ -absorption of nuclear$C$^{∗}-algebras},
  author={Hiroki Matui, and Yasuhiko Sato},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203359482800760},
  booktitle={Acta Mathematica},
  volume={209},
  number={1},
  pages={179-196},
  year={2011},
}
Hiroki Matui, and Yasuhiko Sato. Strict comparison and $$ \mathcal{Z} $$ -absorption of nuclear$C$^{∗}-algebras. 2011. Vol. 209. In Acta Mathematica. pp.179-196. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203359482800760.
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