Generalized derivable mappings at zero point on some reflexive operator algebras
Generalized derivable mappings at zero point on some reflexive operator algebras
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DOI：
10.1016/j.laa.2004.11.012
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发表时间：
2005-03
影响因子：
1.1
通讯作者：
Jun Zhu;Changping Xiong
中科院分区：
文献类型：
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作者：
Jun Zhu;Changping Xiong
设A是B（H）中具有单位算子I的子代数，我们说从A到B（H）的线性映射是在零点广义可导映射，如果对任意S，T∈A，ST=0，有<$（ST）=<$（S）T+S <$（T）−S <$（I）T.本文证明了以下主要结果：有限CSL代数上的每个范数连续的在零点的广义可导映射都是广义导子。
Let A be a subalgebra with the unit operator I in B(H), we say that a linear mapping ϕ from A into B(H) is a generalized derivable mapping at zero point if ϕ(ST)=ϕ(S)T+Sϕ(T)−Sϕ(I)T for any S, T∈A with ST=0. In this paper, we show the following main result: every norm-continuous generalized derivable mapping at zero point on finite CSL algebras is a generalized derivation.