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
  • [11] Decomposition of singular matrices into idempotents
    Alahmadi, Adel
    Jain, S. K.
    Leroy, Andre
    LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (01) : 13 - 27
  • [12] On maps preserving square roots of idempotent and rank-one nilpotent matrices
    Borisov, Nikita
    Julius, Hayden
    Sikora, Martha
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (06)
  • [13] Maps preserving idempotence on spaces of 2x2 symmetric matrices
    Sheng, Yu-Q
    Zheng, Bao-Dong
    PROCEEDINGS OF THE 14TH CONFERENCE OF INTERNATIONAL LINEAR ALGEBRA SOCIETY, 2007, : 241 - 244
  • [14] Maps preserving the idempotency of products of operators
    Fang, Li
    Ji, Guoxing
    Pang, Yongfeng
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 426 (01) : 40 - 52
  • [15] Quasi-permutation singular matrices are products of idempotents
    Alahmadi, Adel
    Jain, S. K.
    Leroy, Andre
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 496 : 487 - 495
  • [16] Additive maps preserving matrices of inner local spectral radius zero at some fixed vector
    Costara, Constantin
    COMPLEX ANALYSIS AND SPECTRAL THEORY, 2020, 743 : 1 - 9
  • [17] LINEAR MAPS PRESERVING THE IDEMPOTENCY OF JORDAN PRODUCTS OF OPERATORS
    Fang, Li
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2011, 22 : 767 - 779
  • [18] Uniquely strongly clean triangular matrices
    Chen, Huanyin
    Gurgun, Orhan
    Kose, Handan
    TURKISH JOURNAL OF MATHEMATICS, 2015, 39 (05) : 645 - 649
  • [19] Matrices over a commutative ring as sums of three idempotents or three involutions
    Tang, Gaohua
    Zhou, Yiqiang
    Su, Huadong
    LINEAR & MULTILINEAR ALGEBRA, 2019, 67 (02) : 267 - 277
  • [20] Maps preserving the truncation of products of operators
    Jia, Xinrong
    Shi, Weijuan
    Ji, Guoxing
    ANNALS OF FUNCTIONAL ANALYSIS, 2022, 13 (03)
12345