摘要
设Q是Hilbert空间H上的非平凡完备套,{dn:n∈N}是H上的一族线性映射。如果dn(ST)=∑i+j=ndi(S)dj(T),S,T∈AlgQ,ST=G,则称dn在G点高阶可导。如果每一个在G点高阶可导的线性映射都是高阶导子,则称G点为高阶全可导点。该文利用数学归纳法证明G∈AlgQ是高阶全可导点当且仅当G≠0。
Let be a complete nest on a Hilbert space .We say that is a higher derivable mapping at if for any with . An element is called a higher all-derivable point of if every higher derivable linear mapping at is a high- er derivation.In this paper, we prove that an operator is a higher all-derivable point if and only if by mathe- matical induction.
出处
《杭州电子科技大学学报（自然科学版）》
2012年第3期87-90,共4页
Journal of Hangzhou Dianzi University：Natural Sciences
关键词
套代数
高阶全可导点
高阶导子
nest algebra
higher all-derivable point
higher derivation
