JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (12): 10-14.doi: 10.6040/j.issn.1671-9352.0.2014.501

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Nonlinear Lie centralizers of generalized matrix algebras

ZHANG Fang-juan   

  1. School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, Shaanxi, China
  • Received:2014-11-10 Revised:2015-04-21 Online:2015-12-20 Published:2015-12-23

Abstract: Let G be a generalized matrix algebra. Assume that Ф:GGis a nonlinear Lie centralizer. It is shown that, under some mild conditions, Ф can be expressed as Ф=φ+τ, where φ:GGis an additive centralizer and τ:GZ(G) is a mapping that vanishes at commutators. Based on the above results, the characterizations of nonlinear Lie centralizers on factor von Neumann algebras, triangular algebras are obtained.

Key words: generalized matrix algebra, nonlinear, Lie centralizer

CLC Number: 

  • O177.1
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