Open Access
2014 On the Bishop-Phelps-Bollobás Property for Numerical Radius
Sun Kwang Kim, Han Ju Lee, Miguel Martín
Abstr. Appl. Anal. 2014(SI20): 1-15 (2014). DOI: 10.1155/2014/479208


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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Sun Kwang Kim. Han Ju Lee. Miguel Martín. "On the Bishop-Phelps-Bollobás Property for Numerical Radius." Abstr. Appl. Anal. 2014 (SI20) 1 - 15, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022458
MathSciNet: MR3198198
Digital Object Identifier: 10.1155/2014/479208

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI20 • 2014
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