三角代数中的Jordan高全可导点
Jordan higher all-derivable points in triangular algebras
摘要：
设${\mathcal{T}}$是一个三角代数。我们说$D=\{D_{n}: n\in N\}\subseteq L({\mathcal{T}})$是在$G$上的Jordan高可导映射，如果对任何具有$ST=G$的$S,T\in {\mathcal{T}}$，有$D_{n}(ST+TS)=\sum_{i+j=n}(D_{i}(S)D_{j}(T)+D_{i}(T)D_{j}(S))$.一个元素$G\in {\mathcal{T}}$称为${\mathcal{T}}$的Jordan高全可导点，如果每个在$G$上的Jordan高可导线性映射$D=\{D_{n}\}_{n\in N}$都是高导子.本文在${\mathcal{T}}$的一些较弱的条件下，证明了${\mathcal{T}}$的某些元素是Jordan高全可导点.这将文[6]中的一些结果推广到Jordan高阶导子的情形。
英文摘要：
Let ${\mathcal{T}}$ be a triangular algebra. We say that $D=\{D_{n}: n\in N\}\subseteq L({\mathcal{T}})$ is a Jordan higher derivable mapping at $G$ if $D_{n}(ST+TS)=\sum_{i+j=n}(D_{i}(S)D_{j}(T)+D_{i}(T)D_{j}(S))$ for any $S,T\in {\mathcal{T}}$ with $ST=G$. An element $G\in {\mathcal{T}}$ is called a Jordan higher all-derivable point of ${\mathcal{T}}$ if every Jordan higher derivable linear mapping $D=\{D_{n}\}_{n\in N}$ at $G$ is a higher derivation. In this paper, under some mild conditions on ${\mathcal{T}}$, we prove that some elements of ${\mathcal{T}}$ are Jordan higher all-derivable points. This extends some results in [6] to the case of Jordan higher derivations.
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