On the Bishop-Phelps-Bollobás Property for Numerical Radius

Sun Kwang Kim, Han Ju Lee and Miguel Martín

Abstract and Applied Analysis, 2014, vol. 2014, 1-15

Abstract:

We study the Bishop-Phelps-Bollobás property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces to ensure the BPBp-nu. Among other results, we show that -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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:479208

DOI: 10.1155/2014/479208

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