Sun Kwang Kim, Han Ju Lee, Miguel Martín
Published 2013-12-30, updated 2014-04-01Version 3
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 $L_1(\mu)$-spaces have this property for every measure $\mu$. 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.
Journal: Abstract and Applied Analysis, Volume 2014, Article ID 479208, 16 pages
On the Bishop-Phelps-Bollobas property for numerical radius in C(K)-spaces
The Bishop-Phelps-Bollobás property for numerical radius in $\ell_1(\mathbb{C})$
Some stability properties for the Bishop--Phelps--Bollobás property for Lipschitz maps
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