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2012 Strict comparison and $ \mathcal{Z} $-absorption of nuclear C-algebras
Hiroki Matui, Yasuhiko Sato
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Acta Math. 209(1): 179-196 (2012). DOI: 10.1007/s11511-012-0084-4


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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Hiroki Matui. Yasuhiko Sato. "Strict comparison and $ \mathcal{Z} $-absorption of nuclear C-algebras." Acta Math. 209 (1) 179 - 196, 2012.


Received: 15 November 2011; Published: 2012
First available in Project Euclid: 31 January 2017

zbMATH: 1277.46028
MathSciNet: MR2979512
Digital Object Identifier: 10.1007/s11511-012-0084-4

Rights: 2012 © Institut Mittag-Leffler

Vol.209 • No. 1 • 2012
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