Hereditary uniform property $Γ$

Huaxin Lin

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arXiv · 2202.05720

Hereditary uniform property $Γ$

Huaxin Lin

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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 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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BibTeX RIS

Huaxin Lin. 2022-05-15. Hereditary uniform property $Γ$. https://arxiv.org/abs/2202.05720

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