JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (06): 83-88.doi: 10.6040/j.issn.1671-9352.0.2015.083

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Generalized Jordan centralizers on CDC-algebras

MA Fei1, ZHANG Jian-hua2, HE Wen1   

  1. 1. College of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, Shaanxi, China;
    2. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2015-02-27 Revised:2015-05-20 Online:2015-06-20 Published:2015-07-31

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Abstract: Let Alg(L) be a CDC-algebra on a Hilbert space H, and φ: AlgL → AlgL be an additive mapping. We prove that if for some positive integer numbers m,n,r≥1, (m+n)φ(Ar+1)=mφ(A)Ar+nArφ(A) hold for all A∈A, then there exists some λ∈Z(AlgL ), such that φ(A)=λA, for all A∈AlgL.

Key words: centralizers, CDC-algebras, additive map

CLC Number: 

  • O177.2
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