Acta Mathematica

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

Hiroki Matui and Yasuhiko Sato

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Abstract

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.

Article information

Source
Acta Math., Volume 209, Number 1 (2012), 179-196.

Dates
Received: 15 November 2011
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485892649

Digital Object Identifier
doi:10.1007/s11511-012-0084-4

Mathematical Reviews number (MathSciNet)
MR2979512

Zentralblatt MATH identifier
1277.46028

Rights
2012 © Institut Mittag-Leffler

Citation

Matui, Hiroki; Sato, Yasuhiko. Strict comparison and $ \mathcal{Z} $-absorption of nuclear C ∗ -algebras. Acta Math. 209 (2012), no. 1, 179--196. doi:10.1007/s11511-012-0084-4. https://projecteuclid.org/euclid.acta/1485892649


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