套代数上广义Jordan导子的刻画  

Characterization of Generalized Jordan Derivations on Nest Algebras

作　　者：王丽[1] 齐霄霏[2] 

机构地区：[1]太原理工大学数学学院,太原030024 [2]山西大学数学科学学院,太原030006

出　　处：《太原理工大学学报》2012年第3期287-290,共4页Journal of Taiyuan University of Technology

基　　金：国家自然科学基金资助项目(11101250)

摘　　要：令N为Banach空间X上的套,AlgN为相应的套代数。设δ:AlgN→AlgN是可加映射。证明了如果存在可加映射τ:AlgN→AlgN,使得映射δ满足条件δ(A2)=δ(A)A+Aτ(A)对任意A∈AlgN成立,并且套N中存在一个非平凡元在X中可补,则δ是可加广义Jordan导子,进而,δ是广义导子。Let N be a nest on a Banach space X,and AlgN be the asso ciated nest algebra.In this paper,we prove that,if there is a nontrivial elem ent in a nest N on a Banach space X which is complemented in X,and if δ：AlgN→AlgN be an additive map satisfying δ（AB）=δ（A）B＋Aτ（B） for some additive map τ：AlgN→AlgN and for all A,B∈AlgN,then τ is an additive deriva tion,and moreover δ is an additive generalized derivation.

关 键 词：套代数 可加导子 广义导子 

分 类 号：O177.1[理学—数学]