INJECTIVE LINEAR MAPS ON τ_∞(F) THAT PRESERVE THE ADDITIVITY OF RAN

Abstract

Abstract. We consider T∞(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 φ such that rank(x + y) = rank(x) + rank(y) implies rank(φ(x + y)) = rank(φ(x)) + rank(φ(y)) for all x, y ∈ T∞(F ).