Abstract

Some geometric properties of the Ces{à}ro function spaces Cp,wC_{p,w}, 1⩽p<∞1\leqslant p<\infty, induced by an arbitrary positive weight function ww on an interval (0,l)(0,l) where 0<l⩽∞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 Cp,wC_{p,w} have diameter 22. Also Cp,wC_{p,w}, 1<p<∞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.

Author information

Contact details are reproduced from the original publication and may be historical.

Damian Kubiak

Mathematics Department, Tennessee Technological University, 110 University Drive, Box 5054, Cookeville, TN 38505, U.S.A.

dkubiak@tntech.edu

Keywords

  • Cesàro function space
  • diameter 2 property
  • weak neighborhoods
  • uniformly non-square points

Mathematics Subject Classification

46E30, 46B20, 46B42

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Suggested citation

D. Kubiak. “Some Geometric Properties of the Cesàro Function Spaces.” Journal of Convex Analysis 21 (2014), No. 1, 189–200. https://doi.org/10.68381/jca21010

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.