@misc{10481/91837,
year = {2024},
month = {4},
url = {https://hdl.handle.net/10481/91837},
abstract = {We prove that there exists an equivalent norm on

with the following properties:

    (1)

    The unit ball of 

contains non-empty relatively weakly open subsets of arbitrarily small diameter;
(2)

The set of Daugavet points of the unit ball of

is weakly dense;
(3)

The set of ccw
-points of the unit ball of

    is norming.

We also show that there are points of the unit ball of
which are not -points, meaning that the space fails the diametral local diameter 2 property. Finally, we observe that the space provides both alternative and new examples that illustrate the differences between the various diametral notions for points of the unit ball of Banach spaces.},
organization = {MICIU/AEI/10.13039/501100011033},
organization = {ERDF/EU: grant PID2021-122126NB-C31},
organization = {Grant PID2021-122126NB-C33},
organization = {Grants PID2019-105011GB-I00 and PID2022-139449NB-I00},
organization = {Junta de Andalucía: grant FQM-0185},
organization = {MCIU/AEI/10.13039/ 501100011033 and ERDF A way of making Europe: grant PGC2018-097286-B-I00},
organization = {Project PROMETEU/2021/070 and the predoctoral contract CIACIF/2021/378)},
organization = {Universitat Politècnica de València},
organization = {MICIU/AEI/10.13039/ 501100011033 Grant CEX2020-001105-M},
organization = {Estonian Research Council grant SJD58},
organization = {Spanish Ministerio de Universidades through a predoctoral contract FPU18/03057},
organization = {French ANR project No. ANR-20-CE40-0006},
organization = {MCIU and the European Social Fund through a “Contrato},
organization = {Predoctoral para la Formación de Doctores, 2019” (PRE2019-089135)},
organization = {Instituto de Matemática Interdisciplinar (IMI)},
organization = {Fundación Séneca: ACyT Región de Murcia grant 21955/PI/22},
organization = {Generalitat Valenciana project CIGE/2022/97},
organization = {Funding for open access publishing: Universidad de Granada/CBUA},
publisher = {Springer Nature},
keywords = {Daugavet points},
keywords = {∆-Points},
keywords = {Points of continuity},
title = {Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and ∆-points},
doi = {10.1007/s13398-024-01596-x},
author = {Cobollo, Christian and Isert, Daniel and López Pérez, Ginés and Martín Suárez, Miguel and Perreau, Yoël and Quero de la Rosa, Alicia and Quilis, Andrés and Rodríguez-Vidanes, Daniel L. and Rueda Zoca, Abraham},
}