Hereditary uniform property $\Gamma$

Huaxin Lin

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arXiv · 2202.05720

Hereditary uniform property $\Gamma$

Huaxin Lin

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Abstract

We study the uniform property $\Gamma$ 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 strict comparison and uniform property $\Gamma$ has tracial approximate oscillation zero and stable rank one. Moreover in this case, its hereditary $C^*$-subalgebras also have a version of uniform property $\Gamma.$ If a separable non-elementary simple amenable $C^*$-algebra $A$ with strict comparison has this hereditary uniform property $\Gamma,$ then $A$ is ${\cal Z}$-stable.

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BibTeX RIS

Huaxin Lin. 2022-02-11. Hereditary uniform property $\Gamma$. https://arxiv.org/abs/2202.05720

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