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

Carlos Bosch and Thomas E. Gilsdorf

International Journal of Mathematics and Mathematical Sciences, 1996, vol. 19, 1-6

Abstract:

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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:470973

DOI: 10.1155/S0161171296001007

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