8. On some local Bishop–Phelps–Bollobás properties
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Publication:5137125
DOI10.1515/9783110656756-008zbMath1480.46013arXiv1905.13552OpenAlexW2947817762MaRDI QIDQ5137125
Martin Mazzitelli, Han Ju Lee, Sheldon Dantas, Sun Kwang Kim
Publication date: 1 December 2020
Published in: The Mathematical Legacy of Victor Lomonosov (Search for Journal in Brave)
Abstract: We continue a line of study about some local versions of Bishop-Phelps-Bollob'as 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 $�eta$ of Lindenstrauss. At the end of the paper, we present a diagram comparing all the existing Bishop-Phelps-Bollob'as type properties with each other. Some open questions are left throughout the article.
Full work available at URL: https://arxiv.org/abs/1905.13552
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