Linear mappings derivable at some nontrivial elements
Linear mappings derivable at some nontrivial elements
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DOI：
10.1016/j.laa.2011.03.041
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发表时间：
2011-10
影响因子：
1.1
通讯作者：
Jiren Zhou
中科院分区：
文献类型：
--
作者：
Jiren Zhou
设A是一个代数，M是一个A-双模。设A是A中的任意元素。一个从A到M的线性映射δ称为在A处可导的，如果对A中的任意S，T，δ（ST）= δ（S）T+ S δ（T），且ST= A。给定一个代数A，如Hilbert空间H上的非交换vonNeumann代数或不可约CDCSL代数，证明了在A中存在一个非平凡幂等元P，使得对任何在P A P中可逆的Q∈ P A P，每个在Q处可导的从A到某个有单位元的A-双模（如A或B（H））的线性映射都是导子.
Suppose that A is an algebra and M is an A-bimodule. Let A be any element in A. A linear mapping δ from A into M is said to be derivable at A if δ (ST)= δ (S) T+ S δ (T) for any S, T in A with ST= A. Given an algebra A, such as a non-abelian von Neumann algebra or an irreducible CDCSL algebra on a Hilbert space H with dimH⩾ 2, we show that there exists a nontrivial idempotent P in A such that for any Q∈ P A P which is invertible in P A P, every linear mapping derivable at Q from A into some unital A-bimodule (for example, A or B (H)) is derivation.