Journal of Convex Analysis 21 (2014), No. 1, 189--200
Copyright Heldermann Verlag 2014
Some Geometric Properties of the Cesàro Function Spaces
Damian Kubiak
Mathematics Department, Tennessee Technological University, 110 University Drive, Box 5054, Cookeville, TN 38505, U.S.A.
dkubiak@tntech.edu
[Abstract-pdf]
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 $C_{p,w}$, $1<p<\infty$ 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.
Keywords: Cesaro function space, diameter 2 property, weak neighborhoods, uniformly non-square points.
MSC: 46E30, 46B20, 46B42
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