The structure of linear zero product and commutativity preservers of C*-algebras

被引：0
|
作者：
Liu, Jung-Hui [1 ]
Li, Lei [2 ]
Shi, Luoyi [3 ]
Wong, Ngai-Ching [4 ]
机构：
[1] Sanming Univ, Sch Informat Engn, 25 Jing Dong Rd, Sanming City 365004, Fujian, Peoples R China
[2] Nankai Univ, Sch Math Sci & LPMC, Tianjin 300071, Peoples R China
[3] Tiangong Univ, Sch Software, Tianjin 300387, Peoples R China
[4] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2021年 / 115卷 / 04期
关键词：
Zero product preservers; Commutativity preservers; Automatic continuity; C*-algebras; ORTHOGONALITY PRESERVERS; DISJOINTNESS PRESERVERS; AUTOMATIC-CONTINUITY; BISEPARATING MAPS; OPERATORS; MAPPINGS;
D O I：
10.1007/s13398-021-01134-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let theta : A(sa) -> B-sa be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) C*-algebras. Suppose. preserves commutativity in two directions (i.e., ab = ba if and only if theta(a)theta(b) = theta(b)theta(a)). We show that theta is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of B, and a real linear Jordan isomorphism J : A(sa) -> B-sa such that theta = hJ.
引用
收藏
页数：6
相关论文
共 50 条
  • [31] Complete orthogonality preservers between C*-algebras
    Garces, Jorge J.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 483 (01)
  • [32] Weakly compact orthogonality preservers on C*-algebras
    Francisco J. Fernández-Polo
    Jorge J. Garcés
    Antonio M. Peralta
    Mathematische Zeitschrift, 2012, 270 : 709 - 723
  • [33] LINEAR PRESERVERS ON STRICTLY UPPER TRIANGULAR MATRIX ALGEBRAS
    Jafarian, Ali A.
    OPERATORS AND MATRICES, 2013, 7 (04): : 947 - 953
  • [34] Weakly compact orthogonality preservers on C*-algebras
    Fernandez-Polo, Francisco J.
    Garces, Jorge J.
    Peralta, Antonio M.
    MATHEMATISCHE ZEITSCHRIFT, 2012, 270 (3-4) : 709 - 723
  • [35] Preservers of the local spectral radius zero of Jordan product of operators
    Elhodaibi, Mhamed
    Saber, Somaya
    TURKISH JOURNAL OF MATHEMATICS, 2021, 45 (02) : 1030 - 1039
  • [36] On zero product determined algebras
    Brice, Daniel
    Huang, Huajun
    LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (02): : 326 - 342
  • [37] Commutativity preserving linear maps on central simple algebras
    Bresar, M
    Semrl, P
    JOURNAL OF ALGEBRA, 2005, 284 (01) : 102 - 110
  • [38] Rank-1 nilpotency linear preservers on nest algebras
    Cui, JL
    Guo, MZ
    Hou, JC
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 377 : 267 - 290
  • [39] Jordan embeddings and linear rank preservers of structural matrix algebras
    Gogic, Ilja
    Tomasevic, Mateo
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2025, 707 : 1 - 48
  • [40] Commutativity Conditions in Algebras with C-equalities
    Oudadess, M.
    COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2012, 3 (01): : 61 - 73
12345