| Title:
|
Some results on order weakly compact operators (English) |
| Author:
|
Aqzzouz, Belmesnaoui |
| Author:
|
Hmichane, Jawad |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
359-367 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. (English) |
| Keyword:
|
order weakly compact operator |
| Keyword:
|
order continuous norm |
| Keyword:
|
discrete vector lattice |
| MSC:
|
46A40 |
| MSC:
|
46B40 |
| MSC:
|
46B42 |
| idZBL:
|
Zbl 1212.46038 |
| idMR:
|
MR2597231 |
| DOI:
|
10.21136/MB.2009.140668 |
| . |
| Date available:
|
2010-07-20T18:09:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140668 |
| . |
| Reference:
|
[1] Aliprantis, C. D., Burkinshaw, O.: Locally Solid Riesz Spaces.Academic Press (1978). Zbl 0402.46005, MR 0493242 |
| Reference:
|
[2] Aliprantis, C. D., Burkinshaw, O.: On weakly compact operators on Banach lattices.Proc. Amer. Math. Soc. 83 (1981), 573-578. Zbl 0452.47038, MR 0627695, 10.1090/S0002-9939-1981-0627695-X |
| Reference:
|
[3] Aliprantis, C. D., Burkinshaw, O.: Dunford-Pettis operators on Banach lattices.Trans. Amer. Math. Soc. 274 (1982), 227-238. Zbl 0498.47013, MR 0670929, 10.1090/S0002-9947-1982-0670929-1 |
| Reference:
|
[4] Dodds, P. G.: o-weakly compact mappings of Riesz spaces.Trans. Amer. Math. Soc. 214 (1975), 389-402. Zbl 0313.46011, MR 0385629 |
| Reference:
|
[5] Groenewegen, G., van Rooij, A.: The modulus of a weakly compact operator.Math. Z. 195 (1987), 473-480. Zbl 0611.47032, MR 0900341, 10.1007/BF01166700 |
| Reference:
|
[6] Meyer-Nieberg, P.: Banach Lattices.Universitext. Springer, Berlin (1991). Zbl 0743.46015, MR 1128093 |
| Reference:
|
[7] Schaefer, H. H.: Banach Lattices and Positive Operators.Springer, Berlin (1974). Zbl 0296.47023, MR 0423039 |
| Reference:
|
[8] Wickstead, A. W.: Extremal structure of cones of operators.Quart. J. Math. Oxford 32 (1981), 239-253. Zbl 0431.47024, MR 0615198, 10.1093/qmath/32.2.239 |
| Reference:
|
[9] Zaanen, A. C.: Riesz Spaces II.North Holland Publishing Company (1983). Zbl 0519.46001, MR 0704021 |
| . |
