| Title:
|
On the class of positive almost weak$^{\star}$ Dunford-Pettis operators (English) |
| Author:
|
Retbi, Abderrahman |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
347-354 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we introduce and study the class of almost weak$^{\star}$ Dunford-Pettis operators. As consequences, we derive the following interesting results: the domination property of this class of operators and characterizations of the wDP$^{\star}$ property. Next, we characterize pairs of Banach lattices for which each positive almost weak$^{\star}$ Dunford-Pettis operator is almost Dunford-Pettis. (English) |
| Keyword:
|
almost weak$^{\star}$ Dunford-Pettis operator |
| Keyword:
|
almost Dunford-Pettis operator |
| Keyword:
|
weak Dunford-Pettis$^{\star}$ property |
| Keyword:
|
positive Schur property |
| Keyword:
|
order continuous norm |
| MSC:
|
46A40 |
| MSC:
|
46B40 |
| idZBL:
|
Zbl 06486998 |
| idMR:
|
MR3390281 |
| DOI:
|
10.14712/1213-7243.2015.128 |
| . |
| Date available:
|
2015-07-09T20:50:02Z |
| Last updated:
|
2017-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144349 |
| . |
| Reference:
|
[1] Aliprantis C.D., Burkinshaw O.: Positive Operators.reprint of the 1985 original, Springer, Dordrecht, 2006. Zbl 1098.47001, MR 2262133 |
| Reference:
|
[2] Chen J.X., Chen Z.L., Guo J.X.: Almost limited sets in Banach lattices.J. Math. Anal. Appl 412 (2014), 547–553; doi 10.1016/j.jmaa.2013.10.085. MR 3145821, 10.1016/j.jmaa.2013.10.085 |
| Reference:
|
[3] Dodds P.G., Fremlin D.H.: Compact operators on Banach lattices.Israel J. Math. 34 (1979), 287–320. MR 0570888, 10.1007/BF02760610 |
| Reference:
|
[4] El Kaddouri A., H'michane J., Bouras K., Moussa M.: On the class of weak* Dunford-Pettis operators.Rend. Circ. Mat. Palermo, 62 (2013), 261–265; doi 10.1007/s12215-013-0122-x. Zbl 1287.46010, MR 3090876, 10.1007/s12215-013-0122-x |
| Reference:
|
[5] Meyer-Nieberg P.: Banach Lattices.Universitext, Springer, Berlin, 1991. Zbl 0743.46015, MR 1128093 |
| Reference:
|
[6] Wnuk W.: Banach Lattices with the weak Dunford-Pettis property.Atti Sem. Mat.Fis. Univ. Modena 42 (1994), no. 1, 227–236. Zbl 0805.46023, MR 1282338 |
| Reference:
|
[7] Wnuk W.: Remarks on J.R. Holub's paper concerning Dunford-Pettis operators.Math. Japon, 38 (1993), 1077–1080. Zbl 0799.47020, MR 1250331 |
| Reference:
|
[8] Wnuk W.: Banach Lattices with Order Continuous Norms.Polish Scientific Publishers, Warsaw, 1999. Zbl 0948.46017 |
| Reference:
|
[9] Wnuk W.: Banach lattices with property of the Schur type - a survey.Confer. Sem. Mat. Univ. Bari 249 (1993), no. 25. MR 1230964 |
| . |
