Mohammadhasani, A., Ilkhanizadeh Manesh, A. (2018). Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$. Advances in Operator Theory, 3(3), 451-458. doi: 10.15352/aot.1709-1225

Ahmad Mohammadhasani; Asma Ilkhanizadeh Manesh. "Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$". Advances in Operator Theory, 3, 3, 2018, 451-458. doi: 10.15352/aot.1709-1225

Mohammadhasani, A., Ilkhanizadeh Manesh, A. (2018). 'Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$', Advances in Operator Theory, 3(3), pp. 451-458. doi: 10.15352/aot.1709-1225

Mohammadhasani, A., Ilkhanizadeh Manesh, A. Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$. Advances in Operator Theory, 2018; 3(3): 451-458. doi: 10.15352/aot.1709-1225

Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$

Receive Date: 06 September 2017,
Revise Date: 03 December 2017,
Accept Date: 03 December 2017

Abstract

A nonnegative real matrix $R\in \textbf{M}_{n,m}$ with the property that all its row sums are one is said to be row stochastic. For $x, y \in \mathbb{R}_{n}$, we say $x$ is right matrix majorized by $y$ (denoted by $x\prec_{r} y$) if there exists an $n$-by-$n$ row stochastic matrix $R$ such that $x=yR$. The relation $\sim_{r}$ on $\mathbb{R}_{n}$ is defined as follows. $x\sim_{r}y$ if and only if $ x\prec_{r} y\prec_{r} x$. In the present paper, we characterize the linear preservers of $\sim_{r}$ on $\mathbb{R}_{n}$, and answer the question raised by F. Khalooei [Wavelet Linear Algebra \textbf{1} (2014), no. 1, 43--50].