Daugavet points and -points in Lipschitz-free spaces

M Jung, AR Zoca - arXiv preprint arXiv:2010.09357, 2020 - arxiv.org
We study Daugavet points and $\Delta $-points in Lipschitz-free Banach spaces. We prove
that, if $ M $ is a compact metric space, then $\mu\in S_ {\mathcal F (M)} $ is a Daugavet …

Asymptotic geometry and Delta-points

TA Abrahamsen, V Lima, A Martiny… - Banach Journal of …, 2022 - Springer
We study Daugavet-and Δ-points in Banach spaces. A norm one element x is a Daugavet-
point (respectively, a Δ-point) if in every slice of the unit ball (respectively, in every slice of …

Delta‐points and their implications for the geometry of Banach spaces

TA Abrahamsen, RJ Aliaga, V Lima… - Journal of the …, 2024 - Wiley Online Library
We show that the Lipschitz‐free space with the Radon–Nikodým property and a Daugavet
point recently constructed by Veeorg is in fact a dual space isomorphic to ℓ 1 ℓ_1 …

Characterizations of Daugavet points and delta-points in Lipschitz-free spaces

T Veeorg - Studia Mathematica, 2023 - impan.pl
Abstract A norm $1 $ element $ x $ of a Banach space is a Daugavet point (respectively, a
$\Delta $-point) if every slice of the unit ball (respectively, every slice of the unit ball …

Diametral notions for elements of the unit ball of a Banach space

M Martín, Y Perreau, AR Zoca - arXiv preprint arXiv:2301.04433, 2023 - arxiv.org
We introduce extensions of $\Delta $-points and Daugavet points in which slices are
replaced by relative weakly open subsets (super $\Delta $-points and super Daugavet …

Daugavet property in projective symmetric tensor products of Banach spaces

M Martín, A Rueda Zoca - Banach Journal of Mathematical Analysis, 2022 - Springer
We show that all the symmetric projective tensor products of a Banach space X have the
Daugavet property provided X has the Daugavet property and either X is an L 1-predual (ie …

Daugavet-and Delta-points in spaces of Lipschitz functions

T Veeorg - arXiv preprint arXiv:2206.03475, 2022 - arxiv.org
A norm one element $ x $ of a Banach space is a Daugavet-point (respectively,~ a $\Delta $-
point) if every slice of the unit ball (respectively,~ every slice of the unit ball containing $ x $) …

The Daugavet and Delta-constants of points in Banach spaces

G Choi, M Jung - arXiv preprint arXiv:2307.10647, 2023 - arxiv.org
We introduce two new notions called the Daugavet constant and $\Delta $-constant of a
point, which measure quantitatively how far the point is from being Daugavet point and …

A relative version of Daugavet-points and the Daugavet property

TA Abrahamsen, RJ Aliaga, V Lima, A Martiny… - arXiv preprint arXiv …, 2023 - arxiv.org
We introduce relative versions of Daugavet-points and the Daugavet property, where the
Daugavet-behavior is localized inside of some supporting slice. These points present …

Computing Borel complexity of some geometrical properties in Banach spaces

G López-Pérez, EM Vañó, AR Zoca - arXiv preprint arXiv:2404.19457, 2024 - arxiv.org
We compute the Borel complexity of some classes of Banach spaces such as different
versions of diameter two properties, spaces satisfying the Daugavet equation or spaces with …