保持因子交换性的可加映射  

Additive Maps Preserving Commutativity up to a Factor

作　　者：崔建莲[1] 侯晋川[2,3] PARK Choonkil 

机构地区：[1]清华大学数学科学系,北京100084 [2]太原理工大学数学系,太原030024 [3]山西师范大学数学系,山西临汾041004 [4]Department of Mathematics,Hanyang University

出　　处：《数学年刊（A辑）》2008年第5期583-590,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10501029;No.10611140471;No.19871069;No.10771157);清华大学基础研究基金(No.Jcpy2005056);山西省自然科学基金(No.2007011016);山西回国留学人员科研基金(No.2007-38);韩国科学工程基金(No.F01-2006-000-10111-0)资助的项目.

摘　　要：设x和y是代数中的两个元．如果存在某个数ξ，使得xy=ξyx，称x和y关于因子ξ交换．给出了标准算子代数间双边保关于因子交换的可加满射的刻画和分类以及C^＊-代数间保关于因子交换的有界线性满射的刻画和分类．Let x and y be two elements in an algebra. If x and y satisfy the algebraic relation xy = ξyx for some scalar ξ, then x and y are commutative up to a factor ξ. This paper first gives a characterization of unital additive surjections between standard operator algebras on real or complex Banach spaces which preserve commutativity up to a factor in both directions. A structure theorem for bounded linear surjections preserving commutativity up to a factor between C^＊-algebras is also obtained.

关 键 词：可加保持 关于因子交换性 C^＊-代数 标准算子代数 

分 类 号：O177.1[理学—数学] O177.3[理学—基础数学]