Mackey convergence and quasi-sequentially webbed spaces
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 part...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000029 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |