On the Bishop-Phelps-Bollobás Property for Numerical Radius

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URI: http://hdl.handle.net/10481/31887
ISSN: 1085-3375
ISSN: 1687-0409
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Autor
Kim, Sun Kwang; Lee, Han Ju; Martín Suárez, Miguel
Editorial
Hindawi Publishing Corporation
Materia
Attaining operators
 
Holomorphic functions
 
Spaces
 
Polynomials
 
Denseness
 
Index
 
Norm
 
Fecha
2014
Referencia bibliográfica
Kim, S.K.; Lee, H.J.; Martín, M. On the Bishop-Phelps-Bollobás Property for Numerical Radius. Abstract and Applied Analysis, 2014: 479208 (2014). [http://hdl.handle.net/10481/31887]
Patrocinador
The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2012R1A1A1006869). The third author was partially supported by Spanish MICINN and FEDER project no. MTM2012-31755 and by Junta de Andalucía and FEDER Grants FQM-185 and P09-FQM-4911.
Resumen
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 -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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