http://dx.doi.org/10.4153/CJM-2013-009-2
15 pages
Published:2013-04-02
Sun Kwang Kim, School of Mathematics, Korea Institute for Advanced Study (KIAS), 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea Han Ju Lee, Department of Mathematics Education, Dongguk University - Seoul, 100-715 Seoul, Republic of Korea
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Abstract
A new characterization of the uniform convexity of
Banach space is obtained in the sense of 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
$\ell_p\times \ell_q$ ($1\lt p, q\lt \infty$).
© Canadian Mathematical Society, 2013
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