Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and ∆-points Cobollo, Christian Isert, Daniel López Pérez, Ginés Martín Suárez, Miguel Perreau, Yoël Quero de la Rosa, Alicia Quilis, Andrés Rodríguez-Vidanes, Daniel L. Rueda Zoca, Abraham Daugavet points ∆-Points Points of continuity 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. 2024-05-16T07:08:37Z 2024-05-16T07:08:37Z 2024-04-22 journal article Cobollo, C., Isert, D., López-Pérez, G. et al. Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and -points. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 96 (2024). [https://doi.org/10.1007/s13398-024-01596-x] https://hdl.handle.net/10481/91837 10.1007/s13398-024-01596-x eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature