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Hereditary uniform property Γ

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Abstract

We study the uniform property Γ for separable simple C*-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple C*-algebra A with the strict comparison and uniform property Γ has tracial approximate oscillation zero and stable rank one. Moreover in this case, its hereditary C*-subalgebras also have a version of uniform property Γ. If a separable non-elementary simple amenable C*-algebra A with strict comparison has this hereditary uniform property Γ, then A is \(\cal{Z}\)-stable.

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Acknowledgements

This work was supported by National Science Foundation of USA (Grant No. DMS-1954600) and the Research Center for Operator Algebras in East China Normal University which is supported by Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Science and Technology Commission of Shanghai Municipality (Grant No. 22DZ2229014).

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  1. Huaxin Lin

    Present address: Department of Mathematics, University of Oregon, Eugene, OR, 97405, USA

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  1. Department of Mathematics, East China Normal University, Shangai, 200062, China

    Huaxin Lin

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Lin, H. Hereditary uniform property Γ. Sci. China Math. 66, 1813–1830 (2023). https://doi.org/10.1007/s11425-022-2005-x

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