Strictly barrelled disks in inductive limits of quasi-(LB)-spaces (Q1922849)

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 a 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.