Quantification of the reciprocal Dunford-Pettis property

TL;DR

This paper establishes a quantitative version of the reciprocal Dunford-Pettis property for Banach spaces of the form C_0(Ω), where Ω is locally compact, providing a more precise understanding of these spaces' properties.

Contribution

It introduces a quantitative framework for the reciprocal Dunford-Pettis property specifically for C_0(Ω) spaces, extending classical results.

Findings

Banach spaces C_0(Ω) satisfy a quantitative reciprocal Dunford-Pettis property

Provides new bounds and measures for this property in C_0(Ω) spaces

Enhances understanding of operator behavior in locally compact space function spaces

Abstract

We prove in particular that Banach spaces of the form $C_0(\Omega)$, where $\Omega$ is a locally compact space, enjoy a quantitative version of the reciprocal Dunford-Pettis property.