因子Von Neumann代数中套子代数上零点保ξ-Lie积映射

摘要

This paper studied the relationship between linear maps preserving ξ-Lie product in subset determined at zero product on nest subalgebras and isomorphism and anti-isomorphism, and proved that if φ satisfies φ([A,B]ξ)=[φ(A),φ(B)]ξfor all A,B∈algMβ with AB≠0,then φis an isomorphism or an anti-isomorphism, where algMβ,algMγbe non-trivial nest subalgebras in factor von Neumann algebra M,φ:algMβ→algMγis a linear bi-jective mapping with property φ(I)=I and ξ≠0,1 is a constant.%研究了因子von Neumann代数中套子代数上由零积确定的子集中保ξ-Lie积的线性映射与同构和反同构的关系。证明了若对任意的A,B∈algMβ且AB≠0满足φ([ A,B]ξ)=[φ( A),φ( B)]ξ,则φ或者是一个同构,或者是一个反同构,其中,algM β和algMγ是因子von Neumann代数M中的两个非平凡套子代数,φ：algM β→algMγ是一个线性双射,满足φ(I)= I且ξ≠0,1是常数。