Work

The dual of ( p , σ ) -weakly summable sequences space and its application

Year: 2026

Type: article

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.

Source: Methods of Functional Analysis and Topology

DOI: 10.31392/mfat-npu26_2.2026.04

Author: Ferradi Athmane

Institution: École Normale Supérieure de Bou Saada

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Direction Générale de la Recherche Scientifique et du Développement Technologique

OpenAlex ID: W7203744087