Article
| Title: | On the class of order almost L-weakly compact operators (English) |
| Author: | El Fahri, Kamal |
| Author: | Khabaoui, Hassan |
| Author: | H'michane, Jawad |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 63 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 459-471 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem. (English) |
| Keyword: | order bounded weakly convergent sequence |
| Keyword: | L-weakly compact set |
| Keyword: | order almost L-weakly compact operator |
| Keyword: | L-weakly compact operator |
| MSC: | 46B42 |
| MSC: | 47B60 |
| MSC: | 47B65 |
| idZBL: | Zbl 07723831 |
| idMR: | MR4577041 |
| DOI: | 10.14712/1213-7243.2023.002 |
| . | |
| Date available: | 2023-04-20T13:51:30Z |
| Last updated: | 2023-10-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151646 |
| . | |
| Reference: | [1] Aliprantis C. D., Burkinshaw O.: Positive Operators.Springer, Dordrecht, 2006. Zbl 1098.47001, MR 2262133 |
| Reference: | [2] Aqzzouz B., Elbour A.: Some new results on the class of AM-compact operators.Rend. Circ. Mat. Palermo (2) 59 (2010), no. 2, 267–275. MR 2670695, 10.1007/s12215-010-0020-4 |
| Reference: | [3] Aqzzouz B., Elbour A., H’michane J.: Some properties of the class of positive Dunford–Pettis operators.J. Math. Anal. Appl. 354 (2009), no. 1, 295–300. MR 2510440, 10.1016/j.jmaa.2008.12.063 |
| Reference: | [4] Aqzzouz B., H'michane J.: The duality problem for the class of order weakly compact operators.Glasg. Math. J. 51 (2009), no. 1, 101–108. MR 2471680, 10.1017/S0017089508004576 |
| Reference: | [5] Bouras K., Lhaimer D., Moussa M.: On the class of almost L-weakly and almost M-weakly compact operators.Positivity 22 (2018), 1433–1443. MR 3863626, 10.1007/s11117-018-0586-1 |
| Reference: | [6] Dodds P. G., Fremlin D. H.: Compact operators on Banach lattices.Israel J. Math. 34 (1979), no. 4, 287–320. MR 0570888, 10.1007/BF02760610 |
| Reference: | [7] Elbour A., Afkir F., Sabiri M.: Some properties of almost L-weakly and almost M-weakly compact operators.Positivity 24 (2020), 141–149. MR 4052686, 10.1007/s11117-019-00671-7 |
| Reference: | [8] El Fahri K., Khabaoui H., H'michane J.: Some characterizations of L-weakly compact sets using the unbounded absolute weak convergence and applications.Positivity 26 (2022), no. 3, Paper No. 42, 13 pages. MR 4412414 |
| Reference: | [9] El Fahri K., Oughajji F. Z.: On the class of almost order (L) sets and applications.Rendiconti del Circolo Matematico di Palermo Series 2 70 (2021), 235–245. MR 4234309 |
| Reference: | [10] Lhaimer D., Bouras K., Moussa M.: On the class of order L-weakly and order M-weakly compact operators.Positivity 25 (2021), no. 4, 1569–1578. MR 4301150, 10.1007/s11117-021-00829-2 |
| Reference: | [11] Meyer-Nieberg P.: Banach Lattices.Universitext, Springer, Berlin, 1991. Zbl 0743.46015, MR 1128093 |
| Reference: | [12] Wnuk W.: Banach lattices with properties of the Schur type---a survey.Confer. Sem. Mat. Univ. Bari (1993), No. 249, 25 pages. MR 1230964 |
| Reference: | [13] Wnuk W.: Remarks on J. R. Holub's paper concerning Dunford–Pettis operators.Math. Japon. 38 (1993), no. 6, 1077–1080. MR 1250331 |
| Reference: | [14] Zabeti O.: Unbounded absolute weak convergence in Banach lattices.Positivity 22 (2018), no. 2, 501–505. MR 3780811, 10.1007/s11117-017-0524-7 |
| Reference: | [15] Zabeti O.: Unbounded continuous operators and unbounded Banach–Saks property in Banach lattices.Positivity 25 (2021), no. 5, 1989–2001. MR 4338556, 10.1007/s11117-021-00858-x |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
