Mackey convergence and quasi-sequentially webbed spaces

Autor:	Thomas E. Gilsdorf
Jazyk:	angličtina
Rok vydání:	1991
Předmět:	webbed space quasi-sequentially webbed space Mackey convergence fast convergence local completeness inductive limit. Mathematics QA1-939
Zdroj:	International Journal of Mathematics and Mathematical Sciences, Vol 14, Iss 1, Pp 17-26 (1991)
Druh dokumentu:	article
ISSN:	0161-1712 1687-0425 01611712
DOI:	10.1155/S0161171291000029
Popis:	The problem of characterizing those locally convex spaces satisfying the Mackey convergence condition is still open. Recently in [4], a partial description was given using compatible webs. In this paper, those results are extended by using quasi-sequentially webbed spaces (see Definition 1). In particular, it is shown that strictly barrelled spaces satisfy the Mackey convergence condition and that they are properly contained in the set of quasi-sequentially webbed spaces. A related problem is that of characterizing those locally convex spaces satisfying the so-called fast convergence condition. A partial solution to this problem is obtained. Several examples are given.
Databáze:	Directory of Open Access Journals
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