Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 479208, 15 pages
http://dx.doi.org/10.1155/2014/479208
Research Article

On the Bishop-Phelps-Bollobás Property for Numerical Radius

1Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of Korea
2Department of Mathematics Education, Dongguk University-Seoul, Seoul 100-715, Republic of Korea
3Departamento de Análisis Mátematico, Facultad de Ciencias, Universidad de Granada, E-18071 Granada, Spain

Received 30 December 2013; Accepted 14 February 2014; Published 6 April 2014

Academic Editor: Manuel Maestre

Copyright © 2014 Sun Kwang Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.