On the Bishop-Phelps-Bollobás property for numerical radius

Sun Kwang Kim; Han Ju Lee; Miguel Martín

doi:10.1155/2014/479208

On the Bishop-Phelps-Bollobás property for numerical radius

Sun Kwang Kim
, Han Ju Lee
, Miguel Martín

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 L 1 -spaces have this property for every measure . 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.

Original language	English
Article number	479208
Journal	Abstract and Applied Analysis
Volume	2014
DOIs	https://doi.org/10.1155/2014/479208
State	Published - 2014

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title = "On the Bishop-Phelps-Bollob{\'a}s property for numerical radius",

abstract = "We study the Bishop-Phelps-Bollob{\'a}s 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 -spaces have this property for every measure . 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-Nikod{\'y}m property (even reflexivity) is not enough to get BPBp-nu.",

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AB - 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 L 1 -spaces have this property for every measure . 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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On the Bishop-Phelps-Bollobás property for numerical radius

Abstract

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