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Quantum AlgebraRings and AlgebrasSpectral Theory and Operator Algebramathscidoc: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.
@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.