| Title:
|
Simple construction of spaces without the Hahn-Banach extension property (English) |
| Author:
|
Kakol, Jerzy |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
623-624 |
| . |
| Category:
|
math |
| . |
| Summary:
|
An elementary construction for an abundance of vector topologies $\xi $ on a fixed infinite dimensional vector space $E$ such that $(E,\xi )$ has not the Hahn-Banach extension property but the topological dual $(E,\xi )'$ separates points of $E$ from zero is given. (English) |
| Keyword:
|
Hahn-Banach extension property |
| Keyword:
|
topological vector space |
| MSC:
|
46A22 |
| idZBL:
|
Zbl 0777.46003 |
| idMR:
|
MR1240183 |
| . |
| Date available:
|
2009-01-08T17:59:04Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118533 |
| . |
| Reference:
|
[1] Duren P.L., Romberg R.C., Shields A.L.: Linear functionals in $H^p$-spaces with $0<p<1$.J. Reine Angew. Math. 238 (1969), 32-60. MR 0259579 |
| Reference:
|
[2] Kalton N.J.: Basic sequences in $F$-spaces and their applications.Proc. Edinburgh Math. Soc. 19 (1974), 151-167. Zbl 0296.46010, MR 0415259 |
| Reference:
|
[3] Kakol J.: Nonlocally convex spaces and the Hahn-Banach extension property.Bull. Acad. Polon. Sci. 33 (1985), 381-393. Zbl 0588.46004, MR 0821575 |
| Reference:
|
[4] Klee V.: Exotic topologies for linear spaces.Proc. Symposium on General Topology and its Relations to Modern Algebra, Prague, 1961. Zbl 0111.10701, MR 0154088 |
| Reference:
|
[5] Shapiro J.H.: Examples of proper closed weakly dense subspaces in non-locally convex $F$-spaces.Israel J. Math. 7 (1969), 369-380. Zbl 0202.39303, MR 0257696 |
| Reference:
|
[6] Wilansky A.: Topics in Functional Analysis.Springer Verlag 45 (1967). Zbl 0156.36103, MR 0223854 |
| . |
