On the Bishop-Phelps-Bollobás Property for Numerical Radius-Reference-Cited by-同舟云学术

On the Bishop-Phelps-Bollobás Property for Numerical Radius

Published:2014 Issue: Volume:2014 Page:1-15
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Kim Sun Kwang¹,Lee Han Ju²^ORCID,Martín Miguel³

Affiliation:

1. Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of Korea

2. Department of Mathematics Education, Dongguk University-Seoul, Seoul 100-715, Republic of Korea

3. Departamento de Análisis Mátematico, Facultad de Ciencias, Universidad de Granada, E-18071 Granada, Spain

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 thatL1μ-spaces have this property for every measureμ. 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.

Funder

National Research Foundation of Korea

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/479208.pdf

Reference26 articles.

1. London Mathematical Society Lecture Note Series 2,1971

2. Denseness of operators which attain their numerical radius

3. Density of numerical radius attaining operators on some reflexive spaces