Strictly barrelled disks in inductive limits of quasi-(LB)-spaces
A strictly barrelled disk B in a Hausdorff locally convex space E is a disk such that the linear span of B with the topology of the Minkowski functional of B is a strictly barrelled space. Valdivia's closed graph theorems are used to show that closed strictly barrelled disk in a quasi-(LB)-spa...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171296001007 |
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| _version_ | 1832547441160749056 |
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| author | Carlos Bosch Thomas E. Gilsdorf |
| author_facet | Carlos Bosch Thomas E. Gilsdorf |
| author_sort | Carlos Bosch |
| collection | DOAJ |
| description | A strictly barrelled disk B in a Hausdorff locally convex space E is
a disk such that the linear span of B with the topology of the Minkowski
functional of B is a strictly barrelled space. Valdivia's closed graph theorems
are used to show that closed strictly barrelled
disk in a quasi-(LB)-space is
bounded. It is shown that a locally strictly
barrelled quasi-(LB)-space is
locally complete. Also, we show that a regular
inductive limit of quasi-(LB)-spaces is locally complete if and only if each closed bounded disk is a strictly
barrelled disk in one of the constituents. |
| format | Article |
| id | doaj-art-74cb29dd8aa241ae83b46dc70604ce2d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-74cb29dd8aa241ae83b46dc70604ce2d2025-02-03T06:44:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119472773210.1155/S0161171296001007Strictly barrelled disks in inductive limits of quasi-(LB)-spacesCarlos Bosch0Thomas E. Gilsdorf1Department of Mathematics I.T.A.M., Río Hondo #1, Col. Tizapán San Angel, D.F., México 01000, MexicoDepartment of Mathematics, University of North Dakota, Grand Forks 58202-8376, ND, USAA strictly barrelled disk B in a Hausdorff locally convex space E is a disk such that the linear span of B with the topology of the Minkowski functional of B is a strictly barrelled space. Valdivia's closed graph theorems are used to show that closed strictly barrelled disk in a quasi-(LB)-space is bounded. It is shown that a locally strictly barrelled quasi-(LB)-space is locally complete. Also, we show that a regular inductive limit of quasi-(LB)-spaces is locally complete if and only if each closed bounded disk is a strictly barrelled disk in one of the constituents.http://dx.doi.org/10.1155/S0161171296001007Quasi-(LB)-spacestrictly barrelled spaceinductive limit. |
| spellingShingle | Carlos Bosch Thomas E. Gilsdorf Strictly barrelled disks in inductive limits of quasi-(LB)-spaces International Journal of Mathematics and Mathematical Sciences Quasi-(LB)-space strictly barrelled space inductive limit. |
| title | Strictly barrelled disks in inductive limits of
quasi-(LB)-spaces |
| title_full | Strictly barrelled disks in inductive limits of
quasi-(LB)-spaces |
| title_fullStr | Strictly barrelled disks in inductive limits of
quasi-(LB)-spaces |
| title_full_unstemmed | Strictly barrelled disks in inductive limits of
quasi-(LB)-spaces |
| title_short | Strictly barrelled disks in inductive limits of
quasi-(LB)-spaces |
| title_sort | strictly barrelled disks in inductive limits of quasi lb spaces |
| topic | Quasi-(LB)-space strictly barrelled space inductive limit. |
| url | http://dx.doi.org/10.1155/S0161171296001007 |
| work_keys_str_mv | AT carlosbosch strictlybarrelleddisksininductivelimitsofquasilbspaces AT thomasegilsdorf strictlybarrelleddisksininductivelimitsofquasilbspaces |