On linear preservers of two-sided gut-majorization on ${𝐌}_{n,m}$

Ilkhanizadeh Manesh, Asma, and Mohammadhasani, Ahmad. "On linear preservers of two-sided gut-majorization on ${\bf M}_{n,m}$." Czechoslovak Mathematical Journal 68.3 (2018): 791-801. <http://eudml.org/doc/294591>.

@article{IlkhanizadehManesh2018,
abstract = {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 $\{\bf M\}_\{n,m\}$.},
author = {Ilkhanizadeh Manesh, Asma, Mohammadhasani, Ahmad},
journal = {Czechoslovak Mathematical Journal},
keywords = {g-row stochastic matrix; gut-majorization; linear preserver; strong linear preserver; two-sided gut-majorization},
language = {eng},
number = {3},
pages = {791-801},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On linear preservers of two-sided gut-majorization on $\{\bf M\}_\{n,m\}$},
url = {http://eudml.org/doc/294591},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Ilkhanizadeh Manesh, Asma
AU - Mohammadhasani, Ahmad
TI - On linear preservers of two-sided gut-majorization on ${\bf M}_{n,m}$
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 791
EP - 801
AB - 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 ${\bf M}_{n,m}$.
LA - eng
KW - g-row stochastic matrix; gut-majorization; linear preserver; strong linear preserver; two-sided gut-majorization
UR - http://eudml.org/doc/294591
ER -