| Title:
|
Some characterizations of weakly compact operator on Banach lattices (English) |
| Author:
|
Aqzzouz, Belmesnaoui |
| Author:
|
Bouras, Khalid |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
901-908 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences. (English) |
| Keyword:
|
weakly compact operator |
| Keyword:
|
order continuous norm |
| Keyword:
|
KB-space |
| MSC:
|
46A40 |
| MSC:
|
46B40 |
| MSC:
|
46B42 |
| idZBL:
|
Zbl 1249.46013 |
| idMR:
|
MR2886245 |
| DOI:
|
10.1007/s10587-011-0057-3 |
| . |
| Date available:
|
2011-12-16T15:35:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141795 |
| . |
| Reference:
|
[1] Aliprantis, Ch. D., Burkinshaw, O.: Positive Operators.Reprint of the 1985 original. Springer, Berlin (2006). Zbl 1098.47001, MR 2262133 |
| Reference:
|
[2] Aqzzouz, B., Nouira, R., Zraoula, L.: About positive Dunford-Pettis operators on Banach lattices.J. Math. Anal. Appl. 324 (2006), 49-59. Zbl 1112.47028, MR 2262455, 10.1016/j.jmaa.2005.10.083 |
| Reference:
|
[3] Aqzzouz, B., Elbour, A.: On the weak compactness of b-weakly compact operators.Positivity 14 (2010), 75-81. Zbl 1198.47034, MR 2596465, 10.1007/s11117-009-0006-7 |
| Reference:
|
[4] Aqzzouz, B., Elbour, A., Hmichane, J.: Some properties of the class of positive Dunford-Pettis operators.J. Math. Anal. Appl. 354 (2009), 295-300. Zbl 1167.47033, MR 2510440, 10.1016/j.jmaa.2008.12.063 |
| Reference:
|
[5] Schaefer, H. H.: Banach Lattices and Positive Operators.Die Grundlehren der mathematischen Wissenschaften 215, Springer-Verlag, Berlin and New York (1974). Zbl 0296.47023, MR 0423039 |
| Reference:
|
[6] Meyer-Nieberg, P.: Banach lattices.Universitext. Springer-Verlag, Berlin (1991). Zbl 0743.46015, MR 1128093 |
| Reference:
|
[7] Wickstead, A. W.: Converses for the Dodds-Fremlin and Kalton-Saab theorems.Math. Proc. Camb. Philos. Soc. 120 (1996), 175-179. Zbl 0872.47018, MR 1373356, 10.1017/S0305004100074752 |
| Reference:
|
[8] Wnuk, W.: Some characterizations of Banach lattices with the Schur property.Congress on Functional Analysis (Madrid, 1988). Rev. Mat. Univ. Complutense Madr. {\it 2}, No. Suppl., (1989), 217-224. Zbl 0717.46018, MR 1057221 |
| Reference:
|
[9] Zaanen, A. C.: Riesz Spaces II.North-Holland Mathematical Library 30, Amsterdam-New York-Oxford, North-Holland Publishing Company (1983). Zbl 0519.46001, MR 0704021 |
| . |
