Geodesic
On the class of positive disjoint weak $p$-convergent operators
Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 409-418
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We introduce and study the disjoint weak $p$-convergent operators in Banach lattices, and we give a characterization of it in terms of sequences in the positive cones. As an application, we derive the domination and the duality properties of the class of positive disjoint weak $p$-convergent operators. Next, we examine the relationship between disjoint weak $p$-convergent operators and disjoint $p$-convergent operators. Finally, we characterize order bounded disjoint weak $p$-convergent operators in terms of sequences in Banach lattices.
We introduce and study the disjoint weak $p$-convergent operators in Banach lattices, and we give a characterization of it in terms of sequences in the positive cones. As an application, we derive the domination and the duality properties of the class of positive disjoint weak $p$-convergent operators. Next, we examine the relationship between disjoint weak $p$-convergent operators and disjoint $p$-convergent operators. Finally, we characterize order bounded disjoint weak $p$-convergent operators in terms of sequences in Banach lattices.
DOI : 10.21136/MB.2023.0160-22
Classification : 46A40, 46B40, 46B42
Keywords: $p$-convergent operator; disjoint $p$-convergent operator; positive Schur property of order $p$; order continuous norm; Banach lattice 
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Retbi, Abderrahman. On the class of positive disjoint weak $p$-convergent operators. Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 409-418. doi: 10.21136/MB.2023.0160-22

[1] Alikhani, M., Fakhar, M., Zafarani, J.: $p$-convergent operators and the $p$-Schur property. Anal. Math. 46 (2020), 1-12. | DOI | MR | JFM

[2] Aliprantis, C. D., Burkinshaw, O.: Positive Operators. Springer, Dordrecht (2006). | DOI | MR | JFM

[3] Castillo, J. M. F., Sánchez, F.: Dunford-Pettis-like properties of continuous vector function spaces. Rev. Mat. Univ. Complutense Madr. 6 (1993), 43-59. | MR | JFM

[4] Chen, D., Chávez-Domínguez, J. A., Li, L.: $p$-converging operators and Dunford-Pettis property of order $p$. J. Math. Anal. Appl. 461 (2018), 1053-1066. | DOI | MR | JFM

[5] Dehghani, M. B., Moshtaghioun, S. M.: On the $p$-Schur property of Banach spaces. Ann. Funct. Anal. 9 (2018), 123-136. | DOI | MR | JFM

[6] Diestel, J.: Sequences and Series in Banach Spaces. Graduate Texts in Mathematics 92. Springer, New York (1984). | DOI | MR | JFM

[7] Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge Studies in Advanced Mathematics 43. Cambridge University Press, Cambridge (1995). | DOI | MR | JFM

[8] Dodds, P. G., Fremlin, D. H.: Compact operators in Banach lattices. Isr. J. Math. 34 (1979), 287-320. | DOI | MR | JFM

[9] Dunford, N., Schwartz, J. T.: Linear Operators. I. General Theory. Pure and Applied Mathematics 7. Interscience Publishers, New York (1958). | MR | JFM

[10] Ghenciu, I.: The $p$-Gelfand-Phillips property in space of operators and Dunford-Pettis like sets. Acta Math. Hung. 155 (2018), 439-457. | DOI | MR | JFM

[11] Wnuk, W.: Banach lattices with the weak Dunford-Pettis property. Atti Semin. Mat. Fis. Univ. Modena 42 (1994), 227-236. | MR | JFM

[12] Zeekoei, E. D., Fourie, J. H.: On $p$-convergent operators on Banach lattices. Acta Math. Sin., Engl. Ser. 34 (2018), 873-890. | DOI | MR | JFM

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