Geodesic
Some Geometric Properties of the Cesàro Function Spaces
Journal of convex analysis, Tome 21 (2014) no. 1, pp. 189-2

Voir la notice de l'article provenant de la source Heldermann Verlag

Some geometric properties of the Ces{\`a}ro function spaces $C_{p,w}$, $1\leqslant p\infty$, induced by an arbitrary positive weight function $w$ on an interval $(0,l)$ where $0 l \leqslant\infty$ are studied in this paper. It is shown that all non-empty relatively weakly open sets in the unit ball of $C_{p,w}$ have diameter $2$. Also $C_{p,w}$, $1p\infty$ is strictly convex but no point of its unit ball is strongly extreme. Moreover, some connections between uniformly non-square points and various geometric properties in general Banach spaces are presented.
Classification : 46E30, 46B20, 46B42
Mots-clés : Cesaro function space, diameter 2 property, weak neighborhoods, uniformly non-square points 
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     title = {Some {Geometric} {Properties} of the {Ces\`aro} {Function} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {189--2},
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     year = {2014},
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D. Kubiak. Some Geometric Properties of the Cesàro Function Spaces. Journal of convex analysis, Tome 21 (2014) no. 1, pp. 189-2. http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a9/