算子代数上的广义导子

Generalized Derivations on an Operator Algebras

设A是B(H)的子代数且含单位算子,φ是A从到自身的线性映射且在Z∈A处广义可导,即S,T∈A且ST=Z时,φ(ST)=φ(S)T+Sφ(T)-Sφ(I)T成立。若φ在Z∈A处广义可导时是广义导子,则称Z是φ在A上的全广义可导点。该文证明了诺伊曼代数的每个可逆元是其上范数拓扑连续线性映射的全广义可导点。

Let be a sub-algebra of with a unit operator,where is a complex separable Hilbert space.We say that a linear mapping from into itself is a generalized derivable mapping at if for any with.We say that an operator is an all-generalized-derivable point of for the norm-topology if every norm-topology continuous generalized derivable mapping at is a generalized derivation.In this paper,we get the following main result: every invertible operator in Von Neumann algebra is an all-generalized point for the norm-topology.