| Title:
|
When $(E,\sigma (E,E'))$ is a $DF$-space? (English) |
| Author:
|
Krassowska, Dorota |
| Author:
|
Śliwa, Wiesƚaw |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
43-44 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(E,t)$ be a Hausdorff locally convex space. Either $(E,\sigma (E,E'))$ or \newline $(E',\sigma (E',E))$ is a $DF$-space iff $E$ is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3]. (English) |
| Keyword:
|
$DF$-spaces |
| Keyword:
|
countably quasibarrelled spaces |
| MSC:
|
46A03 |
| MSC:
|
46A04 |
| MSC:
|
46A05 |
| MSC:
|
46A20 |
| idZBL:
|
Zbl 0782.46006 |
| idMR:
|
MR1173744 |
| . |
| Date available:
|
2009-01-08T17:53:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118468 |
| . |
| Reference:
|
[1] Grothendieck A.: Sur les espaces $(F)$ et $(DF)$.Summa Brasil Math. 3 (1954), 57-123. Zbl 0058.09803, MR 0075542 |
| Reference:
|
[2] Iyahen O., Sunday: Some remarks on countably barrelled and countably quasibarrelled spaces.Proc. Edinburgh Math. Soc. 15 (1966), 295-296. MR 0226357 |
| Reference:
|
[3] Radenovič S.: Some remarks on the weak topology of locally convex spaces.Publ. de l'Institut Math. 44 (1988), 155-157. MR 0995423 |
| Reference:
|
[4] Robertson A., Robertson W.: Topological vector spaces.Cambridge Univ. Press, 1973. Zbl 0423.46001, MR 0350361 |
| Reference:
|
[5] Schaefer H.: Topological vector spaces.Springer-Verlag, New York-Heidelberg-Berlin, 1971. Zbl 0983.46002, MR 0342978 |
| . |
