Chinese Quarterly Journal of Mathematics ›› 2014, Vol. 29 ›› Issue (1): 125-128.doi: 10.13371/j.cnki.chin.q.j.m.2014.01.015

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A Local Characterization of Lie Homomorphisms of Nest Algebras

  

  1. 1. Xianyang Vocational Technical College 2. College of Mathematics and Information Science, Shaanxi Normal University
  • Received:2013-07-15 Online:2014-03-30 Published:2023-02-14
  • About author:YANG Miao-xia(1964-), female, native of Xianyang, Shaanxi, a lecturer of Xianyang Vocational Technical College, engages in functional analysis; ZHANG Jian-hua(1965-), male, native of Yongcheng,Henan, a professor of Shaanxi Normal University, Ph.D., engages in operator algebra. ​
  • Supported by:
    Supported by the Specialized Research Foundation for the Doctoral Program of Universities and Colleges of China(20110202110002)

Abstract: In this paper, linear maps preserving Lie products at zero points on nest algebras are studied. It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism. As an application, the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.

Key words: nest algebra, Lie product, Lie homomorphism

CLC Number: