Linear preservers of weak majorization on ℓ1(I)+, when I is an infinite set

Linear Preservers of Majorization

For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathb...

On Nonlinear Preservers of Weak Matrix Majorization

on nonlinear preservers of weak matrix majorization

Linear preservers of two-sided matrix majorization

For vectors X, <span style="fon...

Linear preservers of Miranda-Thompson majorization on MM;N

Miranda-Thompson majorization is a group-induced cone ordering on $mathbb{R}^{n}$ induced by the group of generalized permutation with determinants equal to 1. In this paper, we generalize Miranda-Thompson majorization on the matrices. For $X$, $Yin M_{m,n}$, $X$ is said to be  Miranda-Thompson majorized by $Y$ (denoted by $Xprec_{mt}Y$) if there exists some $Din rm{Conv(G)}$ s...