Inductive and projective limits of spaces
Inductive duals of distinguished frechet spaces
The purpose of this note is to give an example of a distinguished Fréchet space and a non-distinguished Fréchet space which have the same inductive dual. Accordingly, distinguishedness is a property which is not reflected in the inductive dual. In contrast to this example, it was known that the properties of being quasinormable or having the density condition can be characterized in terms of the inductive dual of a Fréchet space.