Abstract
We study the duality relationship between weak Banach–Saks operators and some other classes of operators.
Similar content being viewed by others
References
Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Reprint of the: Original, p. 2006. Springer, Dordrecht (1985)
Altin, B.: Some property of b-weakly compact operators. Gazi Univ. J. Sci. 18(3), 391–395 (2005)
Alpay, S., Altin, B., Tonyali, C.: On property (b) of vector lattices. Positivity 7(1–2), 135–139 (2003)
Aqzzouz, B., Elbour, A., Hmichane, J.: The duality problem for the class of b-weakly compact operators. Positivity 13(4), 683–692 (2009)
Aqzzouz, B., Elbour, A.: On the duality property for semi-compact operators on Banach lattices. Acta Sci. Math. 77(3–4), 513–524 (2011)
Aqzzouz, B., Elbour, A.: Some characterizations of almost Dunford–Pettis operators and applications. Positivity 15(3), 369–380 (2011). https://doi.org/10.1007/s11117-010-0083-7
Aqzzouz, B., Elbour, A., Wickstead, A.: Positive almost Dunford–Pettis operators and their duality. Positivity 15(2), 185–197 (2011). https://doi.org/10.1007/s11117-010-0050-3
Beauzamy, B.: Proprit de Banach–Saks et modèles tals. Semin. Geom. des Espaces de Banach, Ec. Polytech., Cent. Math., 1977–1978, Expose No. 3, p. 16 (1978). (in French)
Chen, Z.L., Wickstead, A.W.: Some applications of Rademacher sequences in Banach lattices. Positivity 2(2), 171–191 (1998)
Meyer-Nieberg, P.: Banach Lattices. Universitext. Springer, Berlin (1991)
Acknowledgements
The authors would like to thank the referees for their valuable comments which helped to improve the manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Aboutafail, O., H’michane, J., Hafidi, N. et al. On the duality problem for the class of weak Banach–Saks operators. Rend. Circ. Mat. Palermo, II. Ser 70, 793–806 (2021). https://doi.org/10.1007/s12215-020-00533-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12215-020-00533-2
Keywords
- Weak Banach–Saks operator
- Order continuous norm
- KB-space
- Discrete vector lattice
- Positive Schur property
- Schur property