Dentable Point and Ball-Covering Property in Banach Spaces

S. Shang ; Y. Cui

Journal of convex analysis, Tome 25 (2018) no. 3, pp. 1045-1058

Résumé

We prove that if every bounded subset of $X^{*}$ is $w^{*}$-separable, $X$ is compactly locally uniformly convex, $X$ is 2-strictly convex and $X$ is nonsquare, then there exists a sequence $\{x_n\}_{n = 1}^\infty $ of dentable points of $B(X)$ such that $S(X) \subset \mathop \cup _{n = 1}^\infty B(x_n,{r_n})$, where $r_{n} 1$ for all $n\in N$. Moreover, we also prove that if $A$ is a bounded closed convex subset of $X$, then $x\in A$ is a strongly exposed point of $A$ if and only if $x$ is a dentable point of $A$ and $x$ is a $w^{*}$-exposed point of $\overline {{A^{{w^*}}}}$.

Détail

Classification : 46B20
Mots-clés : Compactly locally uniformly convex, ball-covering property, dentable point, nonsquare space, 2-strictly convex space