期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1991
卷号：14
DOI：10.1155/S0161171291000820
出版社：Hindawi Publishing Corporation
摘要：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.
