Nest代数上的在零点广义可导映射

Generalized Derivable Mappings at the Point Zero on Nest Algebras

设A为B（H）的子代数, 是A到B（H）的线性映射,我们说 在0点广义可导（广义双边可导）,如果对任意的S,T∈A且ST=0（ST=0或TS=0）,有 （ST）= （S）T+S （T）-S （I）T.本文主要得到如下结果:（1）有限Nest代数上的每个范数拓扑连续的在0点广义可导的线性映射是广义内导子;（2）若N是完备Nest且H_ H,则algN上的每个范数拓扑连续的在0点广义双边可导的线性映射是广义内导子.

Let A be a subalgebra of B(H), we say that a linear mapping : A→B(H) is a generalized derivable (generalized biderivable) at the point zero if (ST) = (S)T+ S (T) - S(I)T for any S, T ∈ A with ST = 0 (ST = 0 or TS = 0). In this paper, we obtain the following results: (1) Every norm-continuous linear mapping of generalized derivable at the point zero on finite nest algebras is a generalized inner derivation; (2) Let N be a complete nest with H_ H, then every norm-continuous linear mapping of generalized biderivable at the point zero on the nest algebra alg N is a generalized inner derivation.