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Certain additive maps on （m ＋ n ＋ 1）-Power Closed Lie Ideals

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Algebra Colloquium 2014年第1期21卷 81-94页

作者： Kun-Shan Liu Department of Mathematics National Taiwan University Taipei 106 Taiwan

Let R be a prime ring and m, n be fixed non-negative integers such that m＋n ≠ 0. Suppose L is an （m＋m＋1）-power closed Lie ideal, and this means ure＋n＋1 ∈ L for all u ∈ L. If charR = 0 or a prime p 〉 2（m ＋ n）, we characterize the additive maps d： L → R satisfying d（um＋n＋1） = （m -＋n ＋ 1）umd（u）un （resp., d（um＋n＋l） = umd（u）un） for all u ∈ L.

关键词： prime ring k-power closed Lie ideal additive map GPI functional identity

additive maps Preserving the Star Partial Order on B(H)

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Communications in Mathematical Research 2015年第1期31卷 89-96页

作者： Xi Cui Ji Guo-xing Ji You-qing College of Mathematics and Information Science Shaanxi Normal University

Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.

关键词： linear operator star partial order additive map

additive maps Preserving the Truncation of Operators

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Journal of Mathematical Research with Applications 2022年第1期42卷 89-94页

作者： Jie YAO Guoxing JI School of Mathematics and Statistics Shaanxi Normal University

Let H be a complex Hilbert space and B（H） the algebra of all bounded linear operators on H. An operator A is called the truncation of B in B（H） if A = P;BP;, where PA and P;denote projections onto the closures of R（A） and R（A*）, respectively. In this paper,we determine the structures of all additive surjective maps on B（H） preserving the truncation of operators in both directions.

关键词： truncation of operator operator equation additive map preserver

additive maps Preserving{1,2,T}-inverses

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Chinese Quarterly Journal of Mathematics 2009年第4期24卷 590-597页

作者： RONG Jian-ying YUE Qin LIU Xu-qing Department of Foundation Courses Huai'an College of Information TechnologyHuai'an 223003China College of Science Nanjing University of Aeronautics and AstronauticsNanjing 210016China Faculty of Mathematics and Physics Huaiyin Institute of TechnologyHuai'an 223003China

Let F be a field of characteristic not 2 and *** f:Mmn(F)→Mmn(F)be an additive map preserving{1,2,T}-inverse,i.e.f(A)=f(A)f(B)Tf(A),f(B)=f(B)f(A)Tf(B)for any A,B C Mmn(F)with A=ABTA,B=*** this paper,we give the suffi... 详细信息

关键词： additive map preserving{1,2,T}-inverse

additive Rank-1 Preservers Between Hermitian Matrix Spaces Over Quaternion Division Algebra

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Chinese Quarterly Journal of Mathematics 2007年第4期22卷 482-491页

作者： HAN Jing-wen ZHENG Bao-dong Department of Mathematics Tianjin University of Finance and Economics Tianjin 300222 China Department of Mathematics Harbin Institute of Technology Harbin 150001 China

Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.

关键词： additive map quaternion division algebra Hermitian matrix rank