Diametral diameter two properties in Banach spaces

Abraham Rueda Zoca; Gin\'es L\'opez P\'erez; Julio Becerra Guerrero

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Diametral diameter two properties in Banach spaces

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arxiv 1509.02061 v4 pith:EOA2FWBC submitted 2015-09-07 math.FA

Diametral diameter two properties in Banach spaces

Julio Becerra Guerrero , Gin\'es L\'opez P\'erez , Abraham Rueda Zoca This is my paper

classification math.FA

keywords propertiesbanachspacesdiameterdiametralabundancecharacterizationsdaugavet

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The aim of this note is to provide several 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, and we intro- duce 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.

Diametral diameter two properties in Banach spaces

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