On the Bishop-Phelps-Bollobás property for numerical radius

Sun Kwang Kim, Han Ju Lee, Miguel Martín

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article number479208
JournalAbstract and Applied Analysis
Volume2014
DOIs
StatePublished - 2014

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