A strictly barrelled disk Β in a Hausdorff locally convex space Ε is a disk such that the linear span of Β with the topology of the Minkowski functional of Β 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 -(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.
|Number of pages||6|
|Journal||International Journal of Mathematics and Mathematical Sciences|
|State||Published - 1996|
- inductive limit
- strictly barrelled space