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

Dual characterization of the Dieudonne-Schwartz theorem on bounded sets

Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USA

Received 3 August 1982

Copyright © 1983 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.