摘要
设τ(N)是一个原子套代数,φ是τ(N)到自身的线性映射.如果A,B∈τ(N)且AB=I,有(φAB)=φ(A)B+Aφ(B)-Aφ(I)B,则称φ是τ(N)上的单位广义可导映射;如果■T,S∈τ(N)使得A∈τ(N),有φ(A)=AT+SA,则称φ是广义内导子.证明了原子套代数上的每个强算子拓扑连续的单位广义可导映射都是广义内导子.
If τ(N) is a atomic nest algebra, φ is a linear map from τ(N) to itself. If A↓A,B∈τ(N) and AB=I, then φ(AB)=φ(A)B+Aφ(B)-Aφ(I)B, it is said that φ is a generalized derivable mapping at u-nit operator from τ(N) to itself. If there are T,S ∈τ(N) so that A↓A∈τ(N), then φ(A) =AT+SA, it is said that φ is a generalized inner derivation. It is proved that every strong operator topology continuous generalized derivable mapping at unit operator on any atomic nest algebra is a generalized inner derivation.
出处
《纺织高校基础科学学报》
CAS
2008年第3期317-319,共3页
Basic Sciences Journal of Textile Universities
基金
国家自然科学基金资助项目(10571114)
关键词
套代数
单位广义可导映射
广义导子
nest algebra
generalized derivable mappings at unit operator
generalized derivation