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, issue 1

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 L1(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.

Date: 2014
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https://doi.org/10.1155/2014/479208

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:479208

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