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 |
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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. |
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ISSN: | 1085-3375 1687-0409 |
DOI: | 10.1155/2014/479208 |