Abstract
In this paper, we prove that the space of strongly \((r, p, \sigma)\)-summable sequences is the topological dual of the space of \((p, \sigma)\)-weakly summable sequences. As an application, we provide a new proof that an operator \( T: E \to F \) is \((p, \sigma)\)-absolutely continuous if and only if its adjoint \( T^*: F^* \to E^* \) is strongly \((p^*, \sigma)\)-continuous.
Key words: Duality, operator ideal, strongly $p|\sigma$-summable, weakly $ p|\sigma$-summable/
Full Text
Article Information
| Title | The dual of $ (p,\sigma)$-weakly summable sequences space and its application |
| Source | Methods Funct. Anal. Topology, Vol. 32 (2026), no. 2, 139-151 |
| DOI | 10.31392/MFAT-npu26_2.2026.04 |
| Milestones | Received 22/07/2025; Revised 20/09/2025 |
| Copyright | The Author(s) 2026 (CC BY-SA) |
Authors Information
Ferradi Athmane
Department of Mathematics, Ecole Normale Superieure de Bousaada, 28001 Bou Saada, Algeria
Citation Example
Ferradi Athmane, The dual of $ (p,\sigma)$-weakly summable sequences space and its application, Methods Funct. Anal. Topology 32
(2026), no. 2, 139-151.
BibTex
@article {MFAT2279,
AUTHOR = {Ferradi Athmane},
TITLE = {The dual of $ (p,\sigma)$-weakly summable sequences space and its application},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {32},
YEAR = {2026},
NUMBER = {2},
PAGES = {139-151},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_2.2026.04},
URL = {https://mfat.imath.kiev.ua/article/?id=2279},
}
