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 pr...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 Z-stable.展开更多
基金supported by National Science Foundation of USA (Grant No.DMS1954600)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)。
文摘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 Z-stable.
