Journal of Convex Analysis 25 (2018), No. 3, 817--840
Copyright Heldermann Verlag 2018
Diametral Diameter Two Properties in Banach Spaces
Julio Becerra Guerrero
Dep. de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
juliobg@ugr.es
Ginés López-Pérez
Dep. de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
glopezp@ugr.es
Abraham Rueda Zoca
Dep. de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
abrahamrueda@ugr.es
The aim of this note is to provide several new variants of the diameter two properties for Banach spaces. We study such properties looking for the abundance of diametral points, which holds in the setting of Banach spaces with the Daugavet property, for example. For this, we introduce the diametral diameter two properties in Banach spaces, showing for these new properties stability results, inheritance to subspaces and characterizations in terms of finite rank projections.
Keywords: Diameter two properties, diametral points, finite rank projections.
MSC: 46B20, 46B22
[ Fulltext-pdf (162 KB)] for subscribers only.