Equivalent norms with the property (β) of Rolewicz

We extend to the non separable setting many characterizations of the Banach spaces admitting an equivalent norm with the property ( β ) of Rolewicz. These characterizations involve in particular the Szlenk index and asymptotically uniformly smooth or convex norms. This allows to extend easily to the...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2017, Vol.111 (1), p.101-113
Hauptverfasser:	Dilworth, S. J., Kutzarova, D., Lancien, G., Randrianarivony, N. L.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Asymptotic properties Banach space Equivalence Mathematical and Computational Physics Mathematics Mathematics and Statistics Norms Original Paper Texts Theoretical
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	We extend to the non separable setting many characterizations of the Banach spaces admitting an equivalent norm with the property ( β ) of Rolewicz. These characterizations involve in particular the Szlenk index and asymptotically uniformly smooth or convex norms. This allows to extend easily to the non separable case some recent results from the non linear geometry of Banach spaces.
ISSN:	1578-7303 1579-1505
DOI:	10.1007/s13398-016-0278-2