套代数上零点广义Lie可导映射

计算机工程与应用 ›› 2014, Vol. 50 ›› Issue (23): 4-6.

套代数上零点广义Lie可导映射

费秀海，王中华

陕西师范大学数学与信息科学学院，西安 710062

出版日期:2014-12-01 发布日期:2014-12-12

Generalized Lie derivable mappings at zero point on nest algebras

FEI Xiuhai, WANG Zhonghua

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China

Online:2014-12-01 Published:2014-12-12

摘要/Abstract

摘要： 设[N]是Hilbert空间[H]上的一个非平凡套，[f]是套代数[AlgN]上的一个连续广义零点Lie-可导映射，[d]是套代数[AlgN]上的一个连续Lie-导子。证明了，如果[?A,B∈AlgN]且[AB=0]有[f([A,B])=f(A)B-f(B)A+Ad(B)-][Bd(A),]则[f([A,B])=f(A)B-f(B)A+Ad(B)-Bd(A),][?A,B∈AlgN]。

关键词: Lie-导子, 广义Lie-导子, Lie-全可导点, 套代数[AlgN]

Abstract: Let[N]be a non-trivial nest on Hilbert space[H,][f]be a continuous generalized Lie derivable mapping at zero point on nest algebra[AlgN]and[d]be a continuous Lie derivation on nest algebra[AlgN.] In this paper, It is shown that if[f]satisfies[f([A,B])=f(A)B-f(B)A+Ad(B)-Bd(A)]for all[A,B∈AlgN]with[AB=0,]then[f([A,B])=f(A)B-f(B)A+][Ad(B)-Bd(A)]for all[A,B∈AlgN.]

Key words: Lie-derivation, generalized Lie-derivation, Lie-all-derivable point, nest algebra[AlgN]

费秀海，王中华. 套代数上零点广义Lie可导映射[J]. 计算机工程与应用, 2014, 50(23): 4-6.

FEI Xiuhai, WANG Zhonghua. Generalized Lie derivable mappings at zero point on nest algebras[J]. Computer Engineering and Applications, 2014, 50(23): 4-6.