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因子von Neumann代数上的非全局非线性Lie三重可导映射

Non-global Nonlinear Lie Triple Derivable Maps on Factor von Nuemann Algebras
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摘要 设M是Hilbert空间H上维数大于1的因子vonNeumann代数,用代数分解方法证明了:如果非线性映射δ:M→M满足对任意的A,B,C∈M且ABC=0,有δ([[A,B],C])=[[δ(A),B],C]+[[A,δ(B)],C]+[[A,B],δ(C)],则存在可加导子d:M→M,使得对任意的A∈M,有δ(A)=d(A)+τ(A)I,其中τ:CI是一个非线性映射,满足对任意的A,B,C∈M且ABC=0时,有τ([[A,B],C])=0。 Let M be a factor von Neumann algebra with dimension greater than 1 on a Hilbert space H . With the help of algebraic decomposition method,we proved that if a nonlinear map δ: M → M satisfied δ([[A,B],C])=[[δ(A),B],C]+[[A,δ(B)],C]+[[A,B],δ(C)] for any A,B,C∈ M with ABC =0,then there existed an additive derivation d: M → M , such that δ(A)=d(A)+τ(A) I for any A∈ M ,where τ: M CI is a nonlinear map such that τ([[A,B],C])=0 with ABC =0 for any A,B,C∈ M .
作者 苏宇甜 张建华 SU Yutian;ZHANG Jianhua(School of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710119,China)
出处 《吉林大学学报(理学版)》 CAS 北大核心 2019年第4期786-792,共7页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11471199)
关键词 Lie三重可导映射 VONNEUMANN代数 非线性映射 导子 Lie triple derivable map von Neumann algebra nonlinear map derivation
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