| Title:
|
Some characterizations of order weakly compact operator (English) |
| Author:
|
Aqzzouz, Belmesnaoui |
| Author:
|
Elbour, Aziz |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
105-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences. (English) |
| Keyword:
|
order weakly compact operator |
| Keyword:
|
order continuous norm |
| Keyword:
|
discrete Banach lattice |
| Keyword:
|
weakly sequentially continuous lattice operations |
| MSC:
|
46A40 |
| MSC:
|
46B40 |
| MSC:
|
46B42 |
| MSC:
|
47B07 |
| MSC:
|
47B60 |
| idZBL:
|
Zbl 1224.46035 |
| idMR:
|
MR2807713 |
| DOI:
|
10.21136/MB.2011.141454 |
| . |
| Date available:
|
2011-03-31T11:31:21Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141454 |
| . |
| 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.: Positive Operators.Reprint of the 1985 original. Springer, Dordrecht (2006). Zbl 1098.47001, MR 2262133 |
| Reference:
|
[3] Dodds, P. G.: o-weakly compact mappings of Riesz spaces.Trans. Amer. Math. Soc. 214 (1975), 389-402. Zbl 0313.46011, MR 0385629 |
| Reference:
|
[4] Meyer-Nieberg, P.: Banach Lattices.Universitext. Springer, Berlin (1991). Zbl 0743.46015, MR 1128093 |
| Reference:
|
[5] Wickstead, A. W.: Converses for the Dodds-Fremlin and Kalton-Saab Theorems.Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. Zbl 0872.47018, MR 1373356, 10.1017/S0305004100074752 |
| . |
