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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1996-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171296001007 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |