Dual characterization of the Dieudonne-Schwartz theorem on bounded sets - C. Bosch; J. Kucera; K. McKennon (International Journal of Mathematics and Mathematical Sciences)
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.