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arXiv · 1312.7698

On the Bishop-Phelps-Bollobás property for numerical radius

Sun Kwang Kim·Han Ju Lee·Miguel Martín
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Abstract

We study the Bishop-Phelps-Bollobás 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 $L_1(μ)$-spaces have this property for every measure $μ$. 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-Nikodým property (even reflexivity) is not enough to get BPBp-nu.

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Sun Kwang Kim, Han Ju Lee, Miguel Martín. 2014-04-01. On the Bishop-Phelps-Bollobás property for numerical radius. https://doi.org/10.1155/2014%2F479208

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