1. CJM Online first
|Uniform Convexity and Bishop-Phelps-BollobÃ¡s Property|
A new characterization of the uniform convexity of Banach space is obtained in the sense of Bishop-Phelps-BollobÃ¡s theorem. It is also proved that the couple of Banach spaces $(X,Y)$ has the bishop-phelps-bollobÃ¡s property for every banach space $y$ when $X$ is uniformly convex. As a corollary, we show that the Bishop-Phelps-BollobÃ¡s theorem holds for bilinear forms on $\ell_p\times \ell_q$ ($1\lt p, q\lt \infty$).
Keywords:Bishop-Phelps-BollobÃ¡s property, Bishop-Phelps-BollobÃ¡s theorem, norm attaining, uniformly convex