关于广义导子与乘子之积(英文)

On the Products of Generalized Derivation sand Multiplications

设 U是一个环 ,A、B、C、D是环 U中的元素 ,分别定义广义导子 δA,B与乘子τC,D如下 :对于环 U中的任意元素 X,δA,B( X) =AX-XB,τC,D( X) =CX-XD.当环 U为巴拿赫空间 Σ上所有有界线性算子组成的巴拿赫空间时 。

For elements A,B,C,D in a ring U, one defines a generalized derivation δ A,B and a multiplication τ C,D on U by setting δ A,B (X)=AX-XB and τ C,D (X)=CXD for any X in U. In the case when the ring U is the algebra of all bounded operators on a Banach space Σ, we characterize when the products τ C,D δ A,B and δ A,B τ C,D are generalized derivations.