This is an announcement for the paper "On the Bishop-Phelps-Bollobas property for numerical radius" by Sun Kwang Kim, Han Ju Lee and Miguel Martin.
Abstract: We study the Bishop-Phelps-Bollob'as property for numerical radius (in short, BPBp-$\nuu$) and find sufficient conditions for Banach spaces ensuring the BPBp-$\nuu$. 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-$\nuu$. In particular, this shows that the Radon-Nikod'{y}m property (even reflexivity) is not enough to get BPBp-$\nuu$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Submitted from: hanjulee@dongguk.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.7698
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