Strictly Barrelled Disks in Inductive Limits of Quasi-(Lb)-Spaces

Carlos Bosch, Thomas E. Gilsdorf

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)727-732
Number of pages6
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume19
Issue number4
DOIs
StatePublished - 1996

Keywords

  • Quasi-(LB)-space
  • inductive limit
  • strictly barrelled space

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