Computer Engineering and Applications ›› 2016, Vol. 52 ›› Issue (7): 13-16.

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On[ (m,n)]-derivation on nest algebras

ZHANG Haifang1,2, FEI Xiuhai2   

  1. 1.Department of Mathematics, Lincang Teachers’ College, Lincang, Yunnan 677000, China
    2.College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
  • Online:2016-04-01 Published:2016-04-19

套代数上的[(m,n)]-导子

张海芳1,2,费秀海2   

  1. 1.临沧师范高等专科学校 数理系,云南 临沧 677000
    2.陕西师范大学 数学与信息科学学院,西安 710062

Abstract: Let[ m],[n ]be non-zero integers with[ (m+n)(m-n)≠0,][ AlgΝ ]be a nest algebra and[ δ ]be a selfmap on[ AlgΝ.] This paper shows that if[ δ ]satisfies[ mδ(AB)+nδ(BA)=mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A) ]for all[ A,B∈AlgΝ,]then[ δ ]is an additive derivation.

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Key words: nest algebra, [(m,n)]-derivation, derivation, inner derivation

摘要: 设[m]和[n]是任意固定的非零整数且[(m+n)(m-n)≠0],[AlgΝ]是一个套代数,[δ]是[AlgΝ]上的一个自映射。证明了如果对任意的算子[A,][B∈AlgΝ]有[mδ(AB)+nδ(BA)=mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A)],则[δ]是一个导子。

关键词: 套代数, [(m,n)]-导子, 导子, 内导子