Research Article

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

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

DOI: 10.2989/16073606.2025.2596051

Author(s): Fereshteh Hamidi DastjerdiYazd University, Iran, S.M. Sadegh ModarresYazd University, Iran, Mehdi NematiIsfahan University of Technology, Iran, Sima Soltani RenaniIsfahan University of Technology, Iran,

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

Download full text Get new issue alerts

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.

« Berezin number inequalities for 2 × 2 operator matrices and applications

An analogue of Ramanujan’s identity for Bernoulli-Carlitz numbers »

Research Article

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

Abstract

Get new issue alerts for Quaestiones Mathematicae

Latest news

Latest articles