Czechoslovak Mathematical Journal, Vol. 68, No. 3, pp. 791-801, 2018
On linear preservers of two-sided gut-majorization on ${\bf M}_{n,m}$
Asma Ilkhanizadeh Manesh, Ahmad Mohammadhasani
Received December 25, 2016. First published April 11, 2018.
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 ${\bf M}_{n,m}$.
Keywords: g-row stochastic matrix; gut-majorization; linear preserver; strong linear preserver; two-sided gut-majorization
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Affiliations: Asma Ilkhanizadeh Manesh, Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box: 7713936417, Rafsanjan, Iran, e-mail: a.ilkhani@vru.ac.ir; Ahma Mohammadhasani, Department of Mathematics, Sirjan University of technology, Sirjan, Iran, e-mail: a.mohammadhasani53@gmail.com
