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Uniform property $\Gamma $ for certain $\mathrm {C^*}$-algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  10 January 2022

Qingzhai Fan  and
Shan Zhang
Qingzhai Fan*
Affiliation:
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China College of Education, Shanghai Jian Qiao University, Shanghai 201306, China
Shan Zhang
Affiliation:
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China e-mail: 202031010014@stu.shmtu.edu.cn
*
e-mail: qzfan@shmtu.edu.cn
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Abstract

In this paper, let A be an infinite-dimensional stably finite unital simple separable $\mathrm {C^*}$ -algebra. Let $B\subset A$ be a centrally large subalgebra in A such that B has uniform property $\Gamma $ . Then we prove that A has uniform property $\Gamma $ . Let $\Omega $ be a class of stably finite unital $\mathrm {C^*}$ -algebras such that for any $B\in \Omega $ , B has uniform property $\Gamma $ . Then we show that A has uniform property $\Gamma $ for any simple unital $\mathrm {C^*}$ -algebra $A\in \rm {TA}\Omega $ .

Keywords

C*-algebrastracial approximationCuntz semigroup

MSC classification

Primary: 46L35: Classifications of $C^*$-algebras
Secondary: 46L05: General theory of $C^*$-algebras 46L80: $K$-theory and operator algebras (including cyclic theory)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 4 , December 2022 , pp. 1063 - 1070
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Copyright
© Canadian Mathematical Society, 2022

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