Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Diameter two properties
  • diametral points
  • finite rank projections

Mathematics Subject Classification

46B20, 46B22

References

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Suggested citation

J. Becerra Guerrero, G. López-Pérez, A. Rueda Zoca. “Diametral Diameter Two Properties in Banach Spaces.” Journal of Convex Analysis 25 (2018), No. 3, 817–840. https://doi.org/10.68381/jca25056

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.