摘要
本文证明如果θ∈(0,1)是一个无理数,那么对任何ε>0,存在δ>0满足下面的结论:对于任何具有消去性质、严格比较、非空迹态空间和单位元的C^(*)-代数A,任何三个酉元u,v,w∈A,如果‖uv-e2πiθvu‖<δ,‖wuw-1-u-1‖<δ,‖wvw-1-v-1‖<δ,‖w2-1A‖<δ,并且u,v,w满足某种迹条件,那么存在三个酉元u,v,w∈A满足uv-e2πiθvu,wuw-1=u-1,wvw-1=v-1,w2=1A和‖u-u‖<ε,‖v-v‖<ε,‖w-w‖<ε.
We show that ifθ∈(0,1)is an irrational number,then for anyε>0,there existsδ>0 satisfying the following:For any unital C*-algebra A with the cancellation property,strict comparison and nonempty tracial state space,any three unitaries u,v,w∈A such that‖uv-e^(2πiθ)vu‖<δ,‖wuw^(-1)-u~(-1)‖<δ,‖wvw^(-1)-v^(-1)‖<δ,‖w^2-1A‖<δ,and u,v,w satisfy certain trace conditions,there exists a triple of unitaries u,v,w∈A such that uv=e~(2πiθ)vu,wuw~(-1)=u~(-1),wvw~(-1)=v~(-1),w^(2)=1_A and‖u-u‖<ε,‖v-v‖<ε,‖w-w‖<ε.
作者
花家杰
王志杰
HUA Jiajie;WANG Zhijie(College of Data Science,Jiacing University,Jiacing,Zhejiang,314001,P.R.China)
出处
《数学进展》
CSCD
北大核心
2024年第1期177-192,共16页
Advances in Mathematics（China）
基金
Supported by NSFC(Nos.11401256,11501249,11871342)
Zhejiang Provincial Natural Science Foundation of China(No.LQ13A010016)
the Scientific Research Fund of Zhejiang Provincial Education Department(No.Y202249575)。
