International Journal of Mathematics and Mathematical Sciences 
Volume 6 (1983), Issue 1, Pages 189-192
doi:10.1155/S0161171283000174

Dual characterization of the Dieudonne-Schwartz theorem on bounded sets

C. Bosch, J. Kucera, and K. McKennon

 Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USA
Received 3 August 1982

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.