Article
| Title: | Almost demi Dunford--Pettis operators on Banach lattices (English) |
| Author: | Benkhaled, Hedi |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 429-438 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We introduce new concept of almost demi Dunford--Pettis operators. Let $E$ be a Banach lattice. An operator $T$ from $E$ into $E$ is said to be almost demi Dunford--Pettis if, for every sequence $\{x_{n}\}$ in $E_{+}$ such that $x_{n}\rightarrow 0$ in $\sigma(E,E')$ and $\|x_{n}-Tx_{n}\|\rightarrow 0$ as $n\rightarrow \infty$, we have $\|x_{n}\|\rightarrow 0$ as $n\rightarrow \infty$. In addition, we study some properties of this class of operators and its relationships with others known operators. (English) |
| Keyword: | almost demi Dunford--Pettis operator |
| Keyword: | Banach lattice |
| Keyword: | positive Schur property |
| MSC: | 46A40 |
| MSC: | 46B40 |
| MSC: | 46B42 |
| DOI: | 10.14712/1213-7243.2024.007 |
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| Date available: | 2024-11-05T11:45:43Z |
| Last updated: | 2024-11-05 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152623 |
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| Reference: | [1] Abramovich Y. A., Aliprantis C. D.: An Invitation to Operator Theory.Graduate Studies in Mathematics, 50, American Mathematical Society, Providence, 2002. Zbl 1022.47001, MR 1921782, 10.1090/gsm/051/02 |
| Reference: | [2] Aliprantis C. D., Burkinshaw O.: Positive Operators.Pure and Applied Mathematics, 119, Academic Press, Orlando, 1985. Zbl 1098.47001, MR 0809372 |
| Reference: | [3] Aqzzouz B., Elbour A.: Some characterizations of almost Dunford–Pettis operators and applications.Positivity 15 (2011), no. 3, 369–380. MR 2832593, 10.1007/s11117-010-0083-7 |
| Reference: | [4] Aqzzouz B., Elbour A., Wickstead A. W.: Positive almost Dunford–Pettis operators and their duality.Positivity 15 (2011), no. 2, 185–197. MR 2803812, 10.1007/s11117-010-0050-3 |
| Reference: | [5] Benkhaled H., Elleuch A., Jeribi A.: The class of order weakly demicompact operators.Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (2) (2020), no. 2, Paper No. 76, 8 pages. MR 4056881 |
| Reference: | [6] Benkhaled H., Hajji M., Jeribi A.: L-weakly and M-weakly demicompact operators on Banach lattices.Filomat 36 (2022), no. 13, 4319–4329. MR 4554326, 10.2298/FIL2213319B |
| Reference: | [7] Benkhaled H., Hajji M., Jeribi A.: On the class of demi Dunford–Pettis operators.Rend. Circ. Mat. Palermo Ser. (2) 72 (2022), no. 2, 901–911. MR 4559078 |
| Reference: | [8] Benkhaled H., Jeribi A.: On $B$-weakly demicompact operators on Banach lattices.Vladikavkaz. Mat. Zh. 25 (2023), no. 4, 20–28. MR 4680962 |
| Reference: | [9] Guerre-Delabrière S.: Classical Sequences in Banach Spaces.Monographs and Textbooks in Pure and Applied Mathematics, 166, Marcel Dekker, New York, 1992. MR 1197117 |
| Reference: | [10] Meyer-Nieberg P.: Banach Lattices.Universitext, Springer, Berlin, 1991. Zbl 0743.46015, MR 1128093 |
| Reference: | [11] Petryshyn W. V.: Construction of fixed points of demicompact mappings in Hilbert space.J. Math. Anal. Appl. 14 (1966), 276–284. MR 0194942, 10.1016/0022-247X(66)90027-8 |
| Reference: | [12] Wnuk W.: Banach lattice with weak Dunford–Pettis property.Atti Sem. Mat. Fis. Univ. Modena 42 (1994), no. 1, 227–236. MR 1282338 |
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