JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 10-14.doi: 10.6040/j.issn.1671-9352.0.2015.266

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Characterization of Lie centralizers on B(X)

FU Li-na, ZHANG Jian-hua*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Received:2015-06-01 Online:2016-08-20 Published:2016-08-08

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Abstract: Let X be a Banach space over the real or complex number field F with dim X>1 and φ:B(X)→B(X) be an additive map. We prove that if there are positive integers m,n such that (m+n)φ(［A,B］)=m［φ(A),B］+n［A,φ(B)］ holds for all A,B∈B(X), then there exist λ∈F and an additive map h:B(X)→F vanishing on commutators such that φ(A)=λA+h(A)I for all A∈B(X).

Key words: additive map, Lie centralizer, Banach space

CLC Number: 

  • O177.1
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