On the Bishop-Phelps-Bollob\'as property for numerical radius
Functional Analysis
2014-04-02 v3
Abstract
We study the Bishop-Phelps-Bollob\'as property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces ensuring the BPBp-nu. Among other results, we show that -spaces have this property for every measure . On the other hand, we show that every infinite-dimensional separable Banach space can be renormed to fail the BPBp-nu. In particular, this shows that the Radon-Nikod\'{y}m property (even reflexivity) is not enough to get BPBp-nu.
Keywords
Cite
@article{arxiv.1312.7698,
title = {On the Bishop-Phelps-Bollob\'as property for numerical radius},
author = {Sun Kwang Kim and Han Ju Lee and Miguel Martín},
journal= {arXiv preprint arXiv:1312.7698},
year = {2014}
}