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On the Bishop-Phelps-Bollobas Property for Numerical Radiusopen access
- Authors
- Kim, Sun Kwang; Lee, Han Ju; Martin, Miguel
- Issue Date
- 2014
- Publisher
- HINDAWI LTD
- Citation
- ABSTRACT AND APPLIED ANALYSIS, v.2014
- Indexed
- SCIE
SCOPUS
- Journal Title
- ABSTRACT AND APPLIED ANALYSIS
- Volume
- 2014
- ISSN
- 1085-3375
1687-0409
- Abstract
- We study the Bishop-Phelps-Bollobas 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 (mu)-spaces have this property for every measure mu. 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-Nikodym property (even reflexivity) is not enough to get BPBp-nu.
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Related Researcher
- Lee, Han Ju
- College of Education (Department of Mathematics Education)