On some local Bishop-Phelps-Bollobás properties

2019/05/31 by Sheldon Dantas, Sun Kwang Kim, Dantas, Sheldon +6
Computer Science · Mathematics · #Advanced Banach Space Theory #Holomorphic and Operator Theory #Optimization and Variational Analysis #math.FA

paper · pdf · doi:10.48550/arxiv.1905.13552

arxiv created 2019/05/31 · arxiv updated 2019/06/03

Abstract

We continue a line of study about some local versions of Bishop-Phelps-Bollobás type properties for bounded linear operators. We introduce and focus our attention on two of these local properties, which we call L_{p, o} and L_{o, p}, and we explore the relation between them and some geometric properties of the underlying spaces, such as spaces having strict convexity, local uniform rotundity, and property β of Lindenstrauss. At the end of the paper, we present a diagram comparing all the existing Bishop-Phelps-Bollobás type properties with each other. Some open questions are left throughout the article.

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