Maps on infinite triangular matrices preserving idempotents

被引：11
|
作者：
Slowik, Roksana [1 ]
机构：
[1] Silesian Tech Univ, Inst Math, Gliwice, Poland
来源：
LINEAR & MULTILINEAR ALGEBRA | 2014年 / 62卷 / 07期
关键词：
preserver; idempotent; infinite triangular matrix; 15A86; 15A04;
D O I：
10.1080/03081087.2013.801965
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider maps phi of triangular infinite matrices over fields F of characteristic different from 2, that have the following property: x - lambda y is idempotent if and only if phi(x) - lambda phi(y) is idempotent for all lambda is an element of F. We show that every such map is a sum of compositions of some standard maps.
引用
收藏
页码：938 / 964
页数：27
相关论文
共 50 条
  • [41] Maps preserving trace of products of matrices
    Huang, Huajun
    Tsai, Ming-Cheng
    LINEAR & MULTILINEAR ALGEBRA, 2023, 71 (18): : 2962 - 2985
  • [42] CONVEX COMBINATIONS OF INFINITE MATRICES OF MAPS
    POLOTSKII, LI
    SAPIR, MV
    SKORNYAKOV, LA
    ACTA SCIENTIARUM MATHEMATICARUM, 1987, 51 (1-2): : 185 - 189
  • [43] Adjacency preserving maps on matrices and operators
    Petek, T
    Semrl, P
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2002, 132 : 661 - 684
  • [44] Maps on matrices preserving local spectra
    Bendaoud, M.
    Douimi, M.
    Sarih, M.
    LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (07): : 871 - 880
  • [45] ORDER PRESERVING MAPS ON HERMITIAN MATRICES
    Semrl, Peter
    Sourour, Ahmed Ramzi
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2013, 95 (01) : 129 - 132
  • [46] Trace and determinant preserving maps of matrices
    Huang, Huajun.
    Liu, Chih-Neng
    Szokol, Patricia
    Tsai, Ming-Cheng
    Zhang, Jun
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 507 : 373 - 388
  • [47] A note on maps preserving products of matrices
    Lu, Lan
    Wang, Yu
    AIMS MATHEMATICS, 2024, 9 (07): : 17039 - 17062
  • [48] Adjacency preserving maps on hermitian matrices
    Huang, Wen-ling
    Semrl, Peter
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2008, 60 (05): : 1050 - 1066
  • [49] Products of infinite upper triangular quadratic matrices
    Bien, M. H.
    Tam, V. M.
    Tri, D. C. M.
    Truong, L. Q.
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2024, 699 : 59 - 71
  • [50] Spectrum and commutativity preserving mappings on triangular matrices
    Petek, T
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 357 (1-3) : 107 - 122
12345