The geometry of L^p-spaces over atomless measure spaces and the Daugavet property

TL;DR

This paper characterizes L^p-spaces over atomless measure spaces using a geometric property related to the Daugavet property, providing new insights into their structure.

Contribution

It introduces a novel geometric characterization of L^p-spaces over atomless measure spaces connected to the Daugavet property.

Findings

L^p-spaces over atomless measure spaces exhibit a specific p-concavity geometric property.

The geometric property is closely related to the Daugavet property in Banach spaces.

This characterization advances understanding of the structure of L^p-spaces in functional analysis.

Abstract

We show that $L^p$-spaces over atomless measure spaces can be characterized in terms of a $p$-concavity type geometric property that is related with the Daugavet property.