THE STABILITY OF AF-RELATIONS  

作　　者：Jiajie HUA 花家杰(College of Data Science,Jiacing University,Jiacing 314001,China)

机构地区：[1]College of Data Science,Jiacing University,Jiacing 314001,China

出　　处：《Acta Mathematica Scientia》2024年第6期2443-2464,共22页数学物理学报（B辑英文版）

基　　金：supported by the Scientific Research Fund of Zhejiang Provincial Education Department(Y202249575);the National Natural Science Foundation of China(11401256);the Zhejiang Provincial Natural Science Foundation of China(LQ13A010016)。

摘　　要：For given l,s∈N,Λ={ρ_(j)}_(j=i),…,s,ρj∈T,the C^(*)-algebra B:=ε({r_(j)}_(j=1),…,s,Λ,l)is defined to be the universal C^(*)-algebra generated by l unitaries u_(1),…,u_(l) subject to the relations r_(j)(u_(1),…,u_(l))-ρ_(j)=0 for all j=1,…,s,where the r_(j) is monomial in u_(1),…,u_(l) and their inverses for j=1,2,…,s.If B is a unital AF-algebra with a unique tracial state,and K_(0)(B)is a finitely generated group,we say that the relations({r_(j)}_(j=1),…,s,Λ,l)are AF-relations.If the relations({r_(j)}_(j=1),…,s,Λ,l)are AF-relations,we prove that,for any ε>0,there exists a δ>0 satisfying the following:for any unital C^(*)-algebra A with the cancellation property,strict comparison,nonempty tracial state space,and any l unitaries u_(1),u_(2),…,u_(l)∈A satisfying‖r_(j)(u_(1),u_(2),…,u_(l))-ρ_(j)‖<δ,j=1,2,…,s,and certain trace conditions,there exist l unitaries u_(1),u_(2),…,u_(l)∈A such that r_(j)(u_(1),u_(2),…,u_(l))=ρ_(j) for j=1,2,…,s,and‖ui-ui‖<ε for i=1,2,…,l.Finally,we give several applications of the above result.

关 键 词：C^(*)-algebras STABILITY AF-relations UNITARY 

分 类 号：O15[理学—数学]