The diametral strong diameter 2 property of Banach spaces is the same as the Daugavet property

TL;DR

This paper proves that the diametral strong diameter 2 property in Banach spaces is equivalent to the Daugavet property, resolving an open question in functional analysis.

Contribution

It establishes the equivalence between the diametral strong diameter 2 property and the Daugavet property in Banach spaces, answering a previously open problem.

Findings

Confirmed the equivalence of the two properties in Banach spaces

Resolved an open question in the theory of Banach spaces

Contributed to the understanding of geometric properties of Banach spaces

Abstract

We demonstrate the result stated in the title, thus answering an open question asked by Julio Becerra Guerrero, Gin\'es L\'opez-P\'erez and Abraham Rueda Zoca in J. Conv. Anal. \textbf{25}, no. 3 (2018).