Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and ∆-points
![[PDF]](/themes/Mirage2/images/thumbnails/mimes/pdf.png "pdf")
Exportar
Metadatos
Mostrar el registro completo del ítemEditorial
Springer Nature
Materia
Daugavet points ∆-Points Points of continuity
Fecha
2024-04-22Referencia bibliográfica
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]
Resumen
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.
Colecciones
Excepto si se señala otra cosa, la licencia del ítem se describe como Atribución 4.0 Internacional