A Local Characterization of Lie&nbsp;Homomorphisms of Nest Algebras

YANG Miao-xia, ZHANG Jian-hua

doi:10.13371/j.cnki.chin.q.j.m.2014.01.015

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 1: 125 - 128

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.01.015

A Local Characterization of Lie Homomorphisms of Nest Algebras

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1. Xianyang Vocational Technical College 2. College of Mathematics and Information Science, Shaanxi Normal University

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.

Received date: 2013-07-15

Online published: 2023-02-14

Supported by

Supported by the Specialized Research Foundation for the Doctoral Program of Universities and Colleges of China(20110202110002)

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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

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YANG Miao-xia, ZHANG Jian-hua . A Local Characterization of Lie Homomorphisms of Nest Algebras[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(1) : 125 -128 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.01.015

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