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Linear maps that increase majorization order

Is there a characterization of the linear operators $T:R^{d}_{+}\to R^{d}_{+}$ such that: $$ x\prec Tx $$ for all probability distributions $x$, with $\prec$ the majorization order? Thanks Fabio …
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Majorization for vector valued function: looking for literature

Let $x,y\in R^{d}$. A function $f:R^{d}\to R$ is called Schur convex if $$ x\prec y\;\;\rightarrow\;\;f(x)\leq f(y). $$ I am interested in functions $g:R^{d}\to R^{d}$ such that $$ x\prec y\;\;\rig …
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