| Title:
|
Convex-compact sets and Banach discs (English) |
| Author:
|
Monterde, I. |
| Author:
|
Montesinos, V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
773-780 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual $E'$ of a locally convex space $E$ is the $\sigma (E',E)$-closure of the union of countably many $\sigma (E',E)$-relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact. (English) |
| Keyword:
|
weakly compact sets |
| Keyword:
|
convex-compact sets |
| Keyword:
|
Banach discs |
| MSC:
|
46A03 |
| MSC:
|
46A50 |
| idZBL:
|
Zbl 1224.13023 |
| idMR:
|
MR2545655 |
| . |
| Date available:
|
2010-07-20T15:39:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140515 |
| . |
| Reference:
|
[1] Day, M. M.: Normed Linear Spaces.Spriger-Verlag (1973). Zbl 0268.46013, MR 0344849 |
| Reference:
|
[2] Floret, K.: Weakly compact sets.Lecture Notes in Math., Springer-Verlag 801 (1980). Zbl 0437.46006, MR 0576235, 10.1007/BFb0091483 |
| Reference:
|
[3] Grothendieck, A.: Critères de compacité dans les espaces fonctionnels généraux.Amer. J. Math. 74 (1952), 168-186. Zbl 0046.11702, MR 0047313, 10.2307/2372076 |
| Reference:
|
[4] Köthe, G.: Topological Vector Spaces I.Springer-Verlag (1969). MR 0248498 |
| Reference:
|
[5] Pták, V.: A combinatorial lemma on the existence of convex means and its applications to weak compactness.Proc. Symp. Pure Math. VII (Convexity 1963) 437-450. MR 0161128 |
| . |
