| Title:
|
Some properties of short exact sequences of locally convex Riesz spaces (English) |
| Author:
|
Radenović, Stojan |
| Author:
|
Kadelburg, Zoran |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
81-89 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the stability of some properties of locally convex Riesz spaces in connection with subspaces and quotients and also the corresponding three-space-problems. We show that in the richer structure there are more positive answers than in the category of locally convex spaces. (English) |
| Keyword:
|
locally convex Riesz space |
| Keyword:
|
short exact sequence |
| Keyword:
|
three-space-problem |
| MSC:
|
46A04 |
| MSC:
|
46A40 |
| MSC:
|
46M99 |
| idZBL:
|
Zbl 0937.46003 |
| idMR:
|
MR1622978 |
| . |
| Date available:
|
2009-01-08T18:39:11Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118987 |
| . |
| Reference:
|
[1] Bonet J., Dierolf S.: On the lifting of bounded sets in Fréchet spaces.Proc. Edinburgh Math. Soc. 36 (1993), 277-281. Zbl 0792.46001, MR 1221048 |
| Reference:
|
[2] Bonet J., Dierolf S., Fernandez C.: On the three-space-problem for distinguished Fréchet spaces.Bull. Soc. Roy. Sci. Liège 59 (1990), 301-306. Zbl 0713.46001, MR 1070413 |
| Reference:
|
[3] Diaz J.C., Dierolf S., Domanski P., Fernandez C.: On the three-space-problem for dual Fréchet spaces.Bull. Polish Acad. Sci. 40 (1992), 221-224. Zbl 0783.46002, MR 1401875 |
| Reference:
|
[4] Dierolf S.: On the three-space-problem and the lifting of bounded sets.Collect. Math. 44 (1993), 81-89. Zbl 0803.46001, MR 1280727 |
| Reference:
|
[5] Graev M.I.: Theory of topological groups.Uspekhi Mat. Nauk 5 (1950), 3-56. MR 0036245 |
| Reference:
|
[6] Grothendieck A.: Sur les espaces (F) et (DF).Summa Bras. Math. 3 (1954), 57-123. Zbl 0058.09803, MR 0075542 |
| Reference:
|
[7] Husain T., Khaleelulla S.M.: Barrelledness in Topological and Ordered Vector Spaces, Lecture Notes in Mathematics 692.Springer Berlin-Heidelberg-New York (1978). MR 0520916 |
| Reference:
|
[8] Kawai I.: Locally convex lattices.J. Math. Soc. Japan 9 (1957), 281-314. Zbl 0079.32203, MR 0095399 |
| Reference:
|
[9] Köthe G.: Topological Vector Spaces I, $2^{nd}$ ed..Springer Berlin-Heidelberg-New York (1983). MR 0248498 |
| Reference:
|
[10] Meise R., Vogt D.: Einführung in Funktionalanalysis.Vieweg Wiesbaden (1992). MR 1195130 |
| Reference:
|
[11] Peressini A.L.: On topologies in ordered vector spaces.Math. Annalen 144 (1961), 199-223. Zbl 0099.09103, MR 0138982 |
| Reference:
|
[12] Roelcke W., Dierolf S.: On the three-space-problem for topological vector spaces.Collect. Math. 32 (1981), 13-35. Zbl 0489.46002, MR 0643398 |
| Reference:
|
[13] Shaefer H.H.: Topological Vector Spaces.Springer Berlin-Heidelberg-New York (1970). |
| Reference:
|
[14] Wong Y-C., Ng K-F.: Partially Ordered Topological Vector Spaces, Oxford Mathematical Monographs.Clarendon Press Oxford (1973). MR 0454581 |
| . |
