Daugavet property and separability in Banach spaces

TL;DR

This paper characterizes separable Banach spaces with the Daugavet property, explores its presence in tensor products, and introduces related indices to deepen understanding of this geometric property.

Contribution

It provides a new characterization of separable Banach spaces with the Daugavet property and introduces indices related to this property, advancing the theoretical understanding.

Findings

Characterization of separable Banach spaces with the Daugavet property

Analysis of the Daugavet property in tensor products of Banach spaces

Introduction of indices related to the Daugavet property

Abstract

We give a characterisation of the separable Banach spaces with the Daugavet property which is applied to study the Daugavet property in the projective tensor product of an $L$-embedded space with another non-zero Banach space. The former characterisation also motivates the introduction of two indices related to the Daugavet property and a short study of them.