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 …

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 …

L-orthogonality, octahedrality and Daugavet property in Banach spaces

G López-Pérez, AR Zoca - Advances in Mathematics, 2021 - Elsevier
In contrast to the separable case, we prove that the existence of almost L-orthogonal vectors
in a nonseparable Banach space X (octahedrality) does not imply the existence of nonzero …

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 …

On weakly almost square Banach spaces

J Rodríguez, AR Zoca - Proceedings of the Edinburgh Mathematical …, 2023 - cambridge.org
ON WEAKLY ALMOST SQUARE BANACH SPACES Page 1 Proceedings of the Edinburgh
Mathematical Society: page 1 of 19 doi:10.1017/S0013091523000536 ON WEAKLY …

Banach spaces which always produce octahedral spaces of operators

A Rueda Zoca - Collectanea Mathematica, 2024 - Springer
We characterise those Banach spaces X which satisfy that L (Y, X) is octahedral for every
non-zero Banach space Y. They are those satisfying that, for every finite dimensional …

Diameter two properties for spaces of Lipschitz functions

R Haller, A Ostrak, M Põldvere - Journal of Functional Analysis, 2024 - Elsevier
We solve some open problems regarding diameter two properties within the class of Banach
spaces of real-valued Lipschitz functions by using de Leeuw's transform. Namely, we show …

Daugavet points in projective tensor products

S Dantas, M Jung, A Rueda Zoca - The Quarterly Journal of …, 2022 - academic.oup.com
In this paper, we are interested in studying when an element z in the projective tensor
product turns out to be a Daugavet point. We prove first that, under some hypothesis, the …

L-Orthogonal Elements and L-Orthogonal Sequences

A Avilés, G Martínez-Cervantes… - International …, 2023 - academic.oup.com
Given a Banach space, we say that a sequence in the unit ball of is-orthogonal if for every.
On the other hand, an element in the bidual sphere is said to be-orthogonal (to) if for every …

The Daugavet property in spaces of vector-valued Lipschitz functions

AR Zoca - Journal of Functional Analysis, 2024 - Elsevier
We prove that if a metric space M has the finite CEP then F (M)⊗ ˆ π X has the Daugavet
property for every non-zero Banach space X. This applies, for instance, if M is a Banach …