Uniform Convexity and the Bishop–Phelps–Bollobás Property

Kim, Sun Kwang ; Lee, Han Ju

Canadian journal of mathematics, Tome 66 (2014) no. 2, pp. 373-386

Résumé

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 $\left( X,Y \right)$ 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 ${{\ell }_{p}}\,\times \,{{\ell }_{q}}$ $\left( 1\,<p,q\,<\,\infty\right)$ .

Détail

DOI : 10.4153/CJM-2013-009-2

Mots-clés : 46B20, 46B22, Bishop–Phelps–Bollobás property, Bishop–Phelps–Bollobás theorem, norm attaining, uniformly convex

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