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

Autor:	Carlos Bosch, Thomas E. Gilsdorf
Jazyk:	angličtina
Rok vydání:	1996
Předmět:	Quasi-(LB)-space strictly barrelled space inductive limit. Mathematics QA1-939
Zdroj:	International Journal of Mathematics and Mathematical Sciences, Vol 19, Iss 4, Pp 727-732 (1996)
Druh dokumentu:	article
ISSN:	0161-1712 1687-0425 01611712
DOI:	10.1155/S0161171296001007
Popis:	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.
Databáze:	Directory of Open Access Journals
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