| Title:
|
On linear preservers of two-sided gut-majorization on ${\bf M}_{n,m}$ (English) |
| Author:
|
Ilkhanizadeh Manesh, Asma |
| Author:
|
Mohammadhasani, Ahmad |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
791-801 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For $X,Y \in {\bf M}_{n,m}$ it is said that $X$ is gut-majorized by $Y$, and we write $ X\prec _{\rm gut} Y$, if there exists an $n$-by-$n$ upper triangular g-row stochastic matrix $R$ such that $X=RY$. Define the relation $\sim _{\rm gut}$ as follows. $X\sim _{\rm gut}Y$ if $X$ is gut-majorized by $Y$ and $Y$ is gut-majorized by $X$. The (strong) linear preservers of $\prec _{\rm gut}$ on $\mathbb {R}^{n}$ and strong linear preservers of this relation on ${\bf M}_{n,m}$ have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of $\sim _{\rm gut}$ on $\mathbb {R}^{n}$ and ${\bf M}_{n,m}$. (English) |
| Keyword:
|
g-row stochastic matrix |
| Keyword:
|
gut-majorization |
| Keyword:
|
linear preserver |
| Keyword:
|
strong linear preserver |
| Keyword:
|
two-sided gut-majorization |
| MSC:
|
15A04 |
| MSC:
|
15A21 |
| idZBL:
|
Zbl 06986972 |
| idMR:
|
MR3851891 |
| DOI:
|
10.21136/CMJ.2018.0648-16 |
| . |
| Date available:
|
2018-08-09T13:14:15Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147368 |
| . |
| Reference:
|
[1] Armandnejad, A., Manesh, A. Ilkhanizadeh: GUT-majorization and its linear preservers.Electron. J. Linear Algebra 23 (2012), 646-654. Zbl 1253.15040, MR 2966796, 10.13001/1081-3810.1547 |
| Reference:
|
[2] Brualdi, R. A., Dahl, G.: An extension of the polytope of doubly stochastic matrices.Linear Multilinear Algebra 61 (2013), 393-408. Zbl 1269.15034, MR 3003432, 10.1080/03081087.2012.689980 |
| Reference:
|
[3] Hasani, A. M., Radjabalipour, M.: The structure of linear operators strongly preserving majorizations of matrices.Electron. J. Linear Algebra 15 (2006), 260-268. Zbl 1145.15003, MR 2255479, 10.13001/1081-3810.1236 |
| Reference:
|
[4] Hasani, A. M., Radjabalipour, M.: On linear preservers of (right) matrix majorization.Linear Algebra Appl. 423 (2007), 255-261. Zbl 1120.15004, MR 2312405, 10.1016/j.laa.2006.12.016 |
| Reference:
|
[5] Manesh, A. Ilkhanizadeh: On linear preservers of sgut-majorization on $M_{n,m}$.Bull. Iran. Math. Soc. 42 (2016), 471-481. Zbl 1373.15043, MR 3498168 |
| Reference:
|
[6] Manesh, A. Ilkhanizadeh: Right gut-majorization on $M_{n,m}$.Electron. J. Linear Algebra 31 (2016), 13-26. Zbl 1332.15011, MR 3484660, 10.13001/1081-3810.3235 |
| Reference:
|
[7] Manesh, A. Ilkhanizadeh, Armandnejad, A.: Ut-majorization on ${\Bbb R}^n$ and its linear preservers.Operator Theory, Operator Algebras and Applications M. Bastos Operator Theory: Advances and Applications 242, Birkhäuser, Basel (2014), 253-259. Zbl 1318.15016, MR 3243295, 10.1007/978-3-0348-0816-3_15 |
| Reference:
|
[8] Li, C. K., Poon, E.: Linear operators preserving directional majorization.Linear Algebra Appl. 235 (2001), 141-149. Zbl 0999.15030, MR 1810100, 10.1016/S0024-3795(00)00328-1 |
| Reference:
|
[9] Motlaghian, S. M., Armandnejad, A., Hall, F. J.: Linear preservers of row-dense matrices.Czech. Math. J. 66 (2016), 847-858. Zbl 06644037, MR 3556871, 10.1007/s10587-016-0296-4 |
| Reference:
|
[10] Niezgoda, M.: Cone orderings, group majorizations and similarly separable vectors.Linear Algebra Appl. 436 (2012), 579-594. Zbl 1244.26047, MR 2854893, 10.1016/j.laa.2011.07.013 |
| . |
