Injective linear maps on $\mathcal{T}_\infty(F)$ that preserve the additivity of rank
Bull. Korean Math. Soc. 2017 Vol. 54, No. 1, 277-287 https://doi.org/10.4134/BKMS.b160097 Published online November 3, 2016 Printed January 31, 2017
Roksana S{\l}owik Kaszubska 23
Abstract : We consider $\mc T_\infty(F)$ -- the space of upper triangular infinite matrices over a field $F$. We investigate injective linear maps on this space which preserve the additivity of rank, i.e., the maps $\phi$ such that \linebreak $\rank(x+y)=\rank(x)+\rank(y)$ implies $\rank(\phi(x+y))=\rank(\phi(x))+\rank(\phi(y))$ for all $x$, $y\in\mc T_\infty(F)$.
Keywords : rank additivity, linear preserver problem, infinite triangular matrices
