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Search: MSC category 46B22 ( Radon-Nikod{y}m, Kreiin-Milman and related properties [See also 46G10] )

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1. CJM 2013 (vol 66 pp. 373)

Kim, Sun Kwang; Lee, Han Ju
Uniform Convexity and Bishop-Phelps-Bollobás Property
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 $\ell_p\times \ell_q$ ($1\lt p, q\lt \infty$).

Keywords:Bishop-Phelps-Bollobás property, Bishop-Phelps-Bollobás theorem, norm attaining, uniformly convex
Categories:46B20, 46B22

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