Derivable maps and derivational points
Derivable maps and derivational points
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DOI：
10.1016/j.laa.2012.01.027
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发表时间：
2012-06
影响因子：
1.1
通讯作者：
Z. Pan
中科院分区：
文献类型：
--
作者：
Z. Pan
对于一个代数A和一个A-双模M，设L(A，M)是从A到M的所有线性映射的集合，一个映射δ∈L(A，M)称为可导的∈A，如果δ(A)B+Aδ(B)=δ(C)，对所有的A，B，∈A，AB=C，我们称元素C∈A为L(A，M)的导点，如果∀δ∈L(A，M)在C处可导的条件是δ在C处可导，则δ是导子.利用Peirce分解刻画了可导映射，并确定了一些一般双模的导数点。作为特例，我们证明了对于Hilbert空间H上的套代数A，每个0≠C∈A都是L(A，B(H))的导数点。
For an algebra A and an A-bimodule M, let L(A,M) be the set of all linear maps from A to M. A map δ∈L(A,M) is called derivable atC∈A if δ(A)B+Aδ(B)=δ(C), for all A,B∈A with AB=C. We call an element C∈A a derivational point of L(A,M) if ∀δ∈L(A,M) the condition δ is derivable at C implies δ is a derivation. We characterize derivable maps by means of Peirce decompositions and determine derivational points for some general bimodules. As a special case, we see that for a nest algebra A on a Hilbert space H, every 0≠C∈A is a derivational point of L(A,B(H)).