JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (10): 92-96.doi: 10.6040/j.issn.1671-9352.0.2021.056

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Nonlinear maps preserving mixed triple η-products between factors

ZHANG Fang-juan   

  1. School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, Shaanxi, China
  • Published:2022-10-06

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Abstract: Let η∈C\{0,-1}and let φ be a not necessarily linear bijection between two factors, satisfying φ(I)=I and preserving mixed triple η-product. It is showed that φ is a linear *-isomorphism if η is not real and φ is either a linear *-isomorphism or a conjugate linear *-isomorphism if η is real.

Key words: map preserving mixed triple η-product, isomorphism, factor

CLC Number: 

  • O177.1
[1] SEMRL P. Quadratic and quasi-quadratic functionals[J]. Proceeding of the American Mathematical Society, 1993, 119(4):1105-1113.
[2] HUO Donghua, ZHENG Baodong, LIU Hongyu. Nonlinear maps preserving Jordan triple η-*-products[J]. Journal of Mathematical Analysis and Applications, 2015, 430(2):830-844.
[3] ZHAO Yuanyuan, LI Changjing, CHEN Quanyuan. Nonlinear maps preserving mixed product on factors[J]. Bulletin of the Iranian Mathematical Society, 2021, 47(5):1325-1335.
[4] YANG Zhujun, ZHANG Jianhua. Nonlinear maps preserving mixed Lie triple products on factor von Neumann algebras[J]. Annals of Functional Analysis, 2019, 10(3):325-336.
[5] ZHAO Fangfang, LI Changjing. Nonlinear maps preserving the Jordan triple *-product between factors[J]. Indagationes Mathematicae, 2018, 29(2):619-627.
[6] LI Changjing, LU Fangyuan. Nonlinear maps preserving the Jordan triple 1-*-product on von Neumann algebras[J]. Complex Analysis and Operator Theory, 2017, 11(1):109-117.
[7] LI Changjing, CHEN Quanyuan, WANG Ting. Nonlinear maps preserving the Jordan triple *-product on factor von Neumann algebras[J]. Chinese Annals of Mathematics(Series B), 2018, 39(4):633-642.
[8] LI Changjing, LU Fangyuan, WANG Ting. Nonlinear maps preserving the Jordan triple *-product on von Neumann algebras[J]. Annals of Functional Analysis, 2016, 7(3):496-507.
[9] 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, 2014, 57(4):775-784.
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