International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1983 / Article

Open Access

Volume 6 |Article ID 305453 | https://doi.org/10.1155/S0161171283000174

C. Bosch, J. Kucera, K. McKennon, "Dual characterization of the Dieudonne-Schwartz theorem on bounded sets", International Journal of Mathematics and Mathematical Sciences, vol. 6, Article ID 305453, 4 pages, 1983. https://doi.org/10.1155/S0161171283000174

Dual characterization of the Dieudonne-Schwartz theorem on bounded sets

Received03 Aug 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.

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.


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