International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 727-732

Strictly barrelled disks in inductive limits of quasi-(LB)-spaces

Carlos Bosch1 and Thomas E. Gilsdorf2

1Department of Mathematics I.T.A.M., Río Hondo #1, Col. Tizapán San Angel, D.F., México 01000, Mexico
2Department of Mathematics, University of North Dakota, Grand Forks 58202-8376, ND, USA

Received 9 June 1995

Copyright © 1996 Carlos Bosch and Thomas E. Gilsdorf. 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.


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.