因子冯诺依曼代数上保持混合Lie三重ξ-积的非线性映射

doi:10.6040/j.issn.1671-9352.0.2018.257

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (6): 106-111.doi: 10.6040/j.issn.1671-9352.0.2018.257

• • 上一篇

因子冯诺依曼代数上保持混合Lie三重ξ-积的非线性映射

周游¹,张建华^2*

1.曲阜师范大学数学科学学院, 山东曲阜 273165;2.陕西师范大学数学与信息科学学院, 陕西西安 710062

发布日期:2019-06-05
作者简介:周游(1994— ), 女, 硕士研究生, 研究方向为算子代数. E-mail:yzhou201302@163.com*通信作者简介:张建华(1965— ),男, 博士, 教授, 博士生导师, 研究方向为算子代数. E-mail:jhzhang@snnu.edu.cn

Nonlinear maps preserving mixed Lie triple ξ-product on factor von Neumann algebras

ZHOU You¹, ZHANG Jian-hua^2*

1. School of Mathematics Science, Qufu Normal University, Qufu 273165, Shandong, China;
2. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China

Published:2019-06-05

摘要/Abstract

摘要： 设M和N 是2个维数大于1的因子冯诺依曼代数,对于任意一个保持混合Lie三重ξ-积(ξ≠1)的双射Φ:M →N,均有如下形式: A→εΨ(A),其中ε∈{1,-1}, Ψ:M →N 。并且有,当ξ∈R时,Ψ是一个线性或共轭线性*-同构;当ξ∈C\R时,Ψ是一个线性*-同构。

关键词: 混合Lie三重ξ-积, 因子冯诺依曼代数, 保持

Abstract: In this paper, we prove that every bijective map preserving mixed Lie triple ξ-products with ξ≠1 from a factor von Neumann algebra M with dim M >1 into another factor von Neumann algebra N with dim N >1 is of the form A→εΨ(A), where ε∈{1,-1} and Ψ:M→N is a linear or conjugate linear *-isomorphism when ξ∈R and Ψ is a linear *-isomorphism when ξ∈C\R.

Key words: mixed Lie triple ξ-product, factor von Neumann algebras, preserver

中图分类号:

O177.1

周游,张建华. 因子冯诺依曼代数上保持混合Lie三重ξ-积的非线性映射[J]. 《山东大学学报(理学版)》, 2019, 54(6): 106-111.

ZHOU You, ZHANG Jian-hua. Nonlinear maps preserving mixed Lie triple ξ-product on factor von Neumann algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 106-111.

参考文献

[1] BRESAR M, MIERS C R. Commutativity preserving mappings of von Neumann algebras[J]. Canadian Journal of Mathematics, 1993, 45(4):695-708.
[2] JANKO M. A note on Lie product preserving maps on M_n(R)[J]. Mathematica Slovaca, 2016, 66(3):715-720.
[3] YU Xiuping, LU Fangyan. Maps preserving Lie product on B(X)[J]. Taiwanese Journal Mathematics, 2008, 12(3):793-806.
[4] 张芳娟.素*-环上非线性保XY-ξYX^* 积[J].数学学报(中文版),2014, 57(4):775-784. ZHANG Fangjuan. Nonlinear preserving product XY-ξYX on prime *-ring[J]. Acta Mathematica Sinica(Chinese Series), 2014, 57(4):775-784.
[5] ZHANG Jianhua, ZHANG Fangjuan. Nonlinear maps preserving Lie products on factor von Neumann algebras[J]. Linear Algebra and its Applications, 2008, 429(1):18-30.
[6] BAI Zhaofang, DU Shuanping. Maps preserving products XY-YX^* on von Neumann algebras[J]. Journal of Mathematical Analysis and Applications, 2012, 386(1):103-109.
[7] CUI Jianlian, CHOONKIL P. Maps preserving strong skew lie product on factor von Neumann algebras[J]. Acta Mathematica Scientia, 2012, 32(2):531-538.
[8] CUI Jianlian, LI Chi-Kwong. Maps preserving product XY-YX^* on factor von Neumann algebras[J]. Linear Algebra and its Applications, 2009, 431(5-7):833-842.
[9] QI Xiaofei, HOU Jinchuan. Strong skew commutativity preserving maps on von Neumann algebras[J]. Journal of Mathematical Analysis and Applications, 2013, 397(1):362-370.
[10] LIU Lei. Lie triple derivations on factor von Neumann algebras[J]. Bulletin of the Korean Mathematical Society, 2015, 52(2):581-591.
[11] MIERS C R. Lie triple derivations of von Neumann algebras[J]. Proceedings of the American Mathematical Society, 1978, 71(1):57-61.
[12] HUO Donghua, ZHENG Baodong, LIU Hongyu. Nonlinear maps preserving Jordan triple η-*-products[J]. Journal of Mathematical Analysis Applications, 2015, 430(2):830-844.
[13] LI Changjing, LU Fangyan. Nonlinear maps preserving the Jordan triple 1-*-product on von Neumann algebras[J]. Complex Analysis Operator Theory, 2017, 11(1):109-117.
[14] LI Changjing, LU Fangyan, WANG Ting. Nonlinear maps preserving Jordan triple *-product on von Neumann algebras[J]. Annals of Functional Analysis, 2016, 7(3):496-507.

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因子冯诺依曼代数上保持混合Lie三重ξ-积的非线性映射

Nonlinear maps preserving mixed Lie triple ξ-product on factor von Neumann algebras

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