Diametral diameter two properties in Banach spaces

2015/09/07 by Julio Becerra Guerrero, Guerrero, Julio Becerra, Ginés López-Pérez +3 · 1 citation
Mathematics · Computer Science · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1509.02061

Abstract

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.

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• Daugavet- and Delta-points in absolute sums of Banach spaces

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