JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 106-111.doi: 10.6040/j.issn.1671-9352.0.2018.257

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

ZHOU You1, ZHANG Jian-hua2*   

  1. 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

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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

CLC Number: 

  • O177.1
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