The $p$-Daugavet property for function spaces

TL;DR

This paper extends the Daugavet property to p-convex Banach function spaces, demonstrating that no reflexive space possesses this property, thereby broadening understanding of the geometric structure of these spaces.

Contribution

It introduces a p-Daugavet property for function spaces and proves that reflexive spaces do not have this property, extending previous results in the area.

Findings

No reflexive Banach space has the p-Daugavet property.

The p-Daugavet property extends the classical Daugavet property to p-convex spaces.

The analysis applies to related classes of Banach function spaces.

Abstract

A natural extension of the Daugavet property for $p$-convex Banach function spaces and related classes is analysed. As an application, we extend the arguments given in the setting of the Daugavet property to show that no reflexive space falls into this class.