Journal of the
Korean Mathematical Society JKMS

We consider $\mc T_\infty(F)$ -- the space of all infinite upper triangular matrices over a field $F$. We give a description of all linear maps that satisfy the property: if $\rank(x)=1$, then $\rank(\phi(x))=1$ for all $x\in\mc T_\infty(F)$. Moreover, we characterize all injective linear maps on $\mc T_\infty(F)$ such that if $\rank(x)=k$, then $\rank(\phi(x))=k$.

Keywords: linear rank preservers, infinite triangular matrices

MSC numbers: 15A04, 15A03, 15A86