Dual characterization of the Dieudonne-Schwartz theorem on bounded sets
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 t...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171283000174 |
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| _version_ | 1832564134662635520 |
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| author | C. Bosch J. Kucera K. McKennon |
| author_facet | C. Bosch J. Kucera K. McKennon |
| author_sort | C. Bosch |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-92c8794eb07b457abd7918226e9a20cc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-92c8794eb07b457abd7918226e9a20cc2025-02-03T01:11:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016118919210.1155/S0161171283000174Dual characterization of the Dieudonne-Schwartz theorem on bounded setsC. Bosch0J. Kucera1K. McKennon2Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USADepartment of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USADepartment of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USAThe 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.http://dx.doi.org/10.1155/S0161171283000174locally convex spaceinductive and projective limitbarrelled spacebounded set. |
| spellingShingle | C. Bosch J. Kucera K. McKennon Dual characterization of the Dieudonne-Schwartz theorem on bounded sets International Journal of Mathematics and Mathematical Sciences locally convex space inductive and projective limit barrelled space bounded set. |
| title | Dual characterization of the Dieudonne-Schwartz theorem on bounded sets |
| title_full | Dual characterization of the Dieudonne-Schwartz theorem on bounded sets |
| title_fullStr | Dual characterization of the Dieudonne-Schwartz theorem on bounded sets |
| title_full_unstemmed | Dual characterization of the Dieudonne-Schwartz theorem on bounded sets |
| title_short | Dual characterization of the Dieudonne-Schwartz theorem on bounded sets |
| title_sort | dual characterization of the dieudonne schwartz theorem on bounded sets |
| topic | locally convex space inductive and projective limit barrelled space bounded set. |
| url | http://dx.doi.org/10.1155/S0161171283000174 |
| work_keys_str_mv | AT cbosch dualcharacterizationofthedieudonneschwartztheoremonboundedsets AT jkucera dualcharacterizationofthedieudonneschwartztheoremonboundedsets AT kmckennon dualcharacterizationofthedieudonneschwartztheoremonboundedsets |