Dual characterization of the Dieudonne-Schwartz theorem on bounded sets

Abstract

The Dieudonné-Schwartz Theorem on bounded sets in a strict inductive limit is investigated for non-strict inductive limits. Its validity is shown to be closely connected with the problem of whether the projective limit of the strong duals is a strong dual itself. A counter-example is given to show that the Dieudonné-Schwartz Theorem is not in general valid for an inductive limit of a sequence of reflexive, Fréchet spaces.

Keywords

• locally convex space
• inductive and projective limit
• barrelled space
• bounded set.