Faithful representations of infinite-dimensional nilpotent Lie algebras
  For locally convex, nilpotent Lie algebras we construct faithful representations by nilpotent operators on a suitable locally convex space. In the special case of nilpotent Banach-Lie algebras we get norm continuous representations by bounded operators on Banach spaces. 
Ingrid Beltita and Daniel Beltita
math.RT math.FA