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 L1μ-spaces have this property for every measure μ. On the other hand, we show that every infinite-dimensiona...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/479208 |
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| _version_ | 1832558992677666816 |
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| author | Sun Kwang Kim Han Ju Lee Miguel Martín |
| author_facet | Sun Kwang Kim Han Ju Lee Miguel Martín |
| author_sort | Sun Kwang Kim |
| collection | DOAJ |
| description | 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 L1μ-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. |
| format | Article |
| id | doaj-art-4a6baccd097c467daa4408750a6e5726 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4a6baccd097c467daa4408750a6e57262025-02-03T01:31:00ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/479208479208On the Bishop-Phelps-Bollobás Property for Numerical RadiusSun Kwang Kim0Han Ju Lee1Miguel Martín2Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of KoreaDepartment of Mathematics Education, Dongguk University-Seoul, Seoul 100-715, Republic of KoreaDepartamento de Análisis Mátematico, Facultad de Ciencias, Universidad de Granada, E-18071 Granada, SpainWe 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 L1μ-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.http://dx.doi.org/10.1155/2014/479208 |
| spellingShingle | Sun Kwang Kim Han Ju Lee Miguel Martín On the Bishop-Phelps-Bollobás Property for Numerical Radius Abstract and Applied Analysis |
| title | On the Bishop-Phelps-Bollobás Property for Numerical Radius |
| title_full | On the Bishop-Phelps-Bollobás Property for Numerical Radius |
| title_fullStr | On the Bishop-Phelps-Bollobás Property for Numerical Radius |
| title_full_unstemmed | On the Bishop-Phelps-Bollobás Property for Numerical Radius |
| title_short | On the Bishop-Phelps-Bollobás Property for Numerical Radius |
| title_sort | on the bishop phelps bollobas property for numerical radius |
| url | http://dx.doi.org/10.1155/2014/479208 |
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