套代数上的单位广义可导映射

Generalized derivable mappings at unit operator on nest algebras

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.