On the Bishop-Phelps-Bollobás Property for Numerical Radius

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 L 1 μ -spaces have this property for every measure μ. On the other hand, we show that every infinite-dimensi...

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Veröffentlicht in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.225-239-723
Hauptverfasser: Kim, Sun Kwang, Martin, Miguel, Lee, Han Ju
Format: Artikel
Sprache:eng
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Zusammenfassung: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 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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/479208