2022/02/11 by Lin, Huaxin
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2202.05720
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.