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http://dx.doi.org/10.4134/BKMS.b160097

INJECTIVE LINEAR MAPS ON τ∞(F) THAT PRESERVE THE ADDITIVITY OF RANK  

Slowik, Roksana (Institute of Mathematics Silesian University of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 277-287 More about this Journal
Abstract
We consider ${\tau}_{\infty}(F)$ - 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 rank(x + y) = rank(x) + rank(y) implies rank(${\phi}(x+y)$) = rank(${\phi}(x)$) + rank(${\phi}(y)$) for all $x,\;y{\in}{\tau}_{\infty}(F)$.
Keywords
rank additivity; linear preserver problem; infinite triangular matrices;
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Times Cited By KSCI : 1  (Citation Analysis)
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