Uniform convexity and the Bishop-Phelps-Bollobás property

Sun Kwang Kim; Han Ju Lee

doi:10.4153/CJM-2013-009-2

Uniform convexity and the Bishop-Phelps-Bollobás property

Sun Kwang Kim, Han Ju Lee

Department of Mathematics Education

Korea Institute for Advanced Study

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

36 Scopus citations

Abstract

A new characterization of the uniform convexity of Banach space is obtained in the sense of the Bishop-Phelps-Bollobás theorem. It is also proved that the couple of Banach spaces (X, Y) has the Bishop-Phelps-Bollobás property for every Banach space Y when X is uniformly convex. As a corollary, we show that the Bishop-Phelps-Bollobás theorem holds for bilinear forms on ℓ_p × ℓ (1<p,q> ∞).

Original language	English
Pages (from-to)	373-386
Number of pages	14
Journal	Canadian Journal of Mathematics
Volume	66
Issue number	2
DOIs	https://doi.org/10.4153/CJM-2013-009-2
State	Published - Apr 2014

Keywords

Bishop-Phelps-Bollobás property
Bishop-Phelps-Bollobás theorem
Norm attaining
Uniformly convex

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10.4153/CJM-2013-009-2

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abstract = "A new characterization of the uniform convexity of Banach space is obtained in the sense of the Bishop-Phelps-Bollob{\'a}s theorem. It is also proved that the couple of Banach spaces (X, Y) has the Bishop-Phelps-Bollob{\'a}s property for every Banach space Y when X is uniformly convex. As a corollary, we show that the Bishop-Phelps-Bollob{\'a}s theorem holds for bilinear forms on ℓp × ℓ (1 ∞).",

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AB - A new characterization of the uniform convexity of Banach space is obtained in the sense of the Bishop-Phelps-Bollobás theorem. It is also proved that the couple of Banach spaces (X, Y) has the Bishop-Phelps-Bollobás property for every Banach space Y when X is uniformly convex. As a corollary, we show that the Bishop-Phelps-Bollobás theorem holds for bilinear forms on ℓp × ℓ (1 ∞).

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KW - Norm attaining

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ER -

Uniform convexity and the Bishop-Phelps-Bollobás property

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Keywords

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