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On the Bishop‐Phelps‐Bollobás Property for Numerical Radius

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  • Sun Kwang Kim
  • Han Ju Lee
  • Miguel Martín

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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:479208
DOI: 10.1155/2014/479208
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