摘要
设Ａ为Ｂａｎａｃｈ空间中一标准算子代数，证明了Ａ到Ｂ（Ｘ）的每一广义导子都是广义内导子，进而，如果线性映射δ：Ａ→Ｂ（Ｘ）满足δ（Ｐ）＝δ（Ｐ）Ｐ＋Ｐδ（Ｐ）－Ｐδ（Ｉ）Ｐ，Ｐ∈Ａ为幂等元，则δ为广义导子．特别地。
Let A be a standard operator algebra in Banach space X , it is proved that every generalized derivation of A into B(X) is a generalized inner derivation. Furthermore, if linear mapping δ :A→ B(X) satisfying δ(P)=δ(P)P+Pδ(P)-Pδ(I)P for each idempotent P ∈A, then δ is a generalized derivation. In particular, every local generalized derivation of A is a generalized derivation.
出处
《曲阜师范大学学报（自然科学版）》
CAS
1999年第2期33-36,共4页
Journal of Qufu Normal University(Natural Science)
基金
烟台师范学院青年科学基金
关键词
标准算子代数
广义导子
局部广义导子
算子代数
standard operator algebra
generalized derivation
local generalized derivation
generalized inner derivation
