This is an announcement for the paper "On the dual of Ces`aro function space" by Anna Kaminska and Damian Kubiak.
Abstract: The goal of this paper is to present an isometric representation of the dual space to Ces`aro function space $C_{p,w}$, $1<p<\infty$, induced by arbitrary positive weight function $w$ on interval $(0,l)$ where $0<l\leqslant\infty$. For this purpose given a strictly decreasing nonnegative function $\Psi$ on $(0,l)$, the notion of essential $\Psi$-concave majorant $\hat f$ of a measurable function $f$ is introduced and investigated. As applications it is shown that every slice of the unit ball of the Ces`aro function space has diameter 2. Consequently Ces`aro function spaces do not have the Radon-Nikodym property, are not locally uniformly convex and they are not dual spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46B42, 46B22
Remarks: 15 pages
Submitted from: dmkubiak@memphis.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.5400
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