Research Article

Dunford-Pettis elements of Banach modules and their applications over commutative Banach algebras

Published in: Quaestiones Mathematicae
Volume 49 , issue 4 , 2026 , pages: 473–487

DOI: 10.2989/16073606.2025.2596051

Author(s): Fereshteh Hamidi Dastjerdi Yazd University, Iran , S.M. Sadegh Modarres Yazd University, Iran , Mehdi Nemati Isfahan University of Technology, Iran , Sima Soltani Renani Isfahan University of Technology, Iran

Keywords: 46B20 , 42B35 , 46J10 , 43A30 , Banach modules , commutative Banach algebras , Dunford-Pettis operators , Fourier algebra , group algebra

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Abstract

Recent research on Dunford-Pettis operators associated with the group algebra L ¹ (G) and the Fourier algebra A(G) of a locally compact group has motivated the study of the structure of the Dunford-Pettis space for a Banach module ϵ over a Banach algebra . In this paper, we study conditions under which (ϵ) coincides with the entire Banach right -module ϵ, and investigate its connections with some classical geometric properties. We analyze the structure of Dunford-Pettis elements for various classical Banach spaces and study their behavior under continuous homomorphisms and quotient maps. Moreover, we explore the geometric properties of certain ideals in commutative Banach algebras.

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