Geodesic
A note on the structure of WUR Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 399-408

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We present an example of a Banach space $E$ admitting an equivalent weakly uniformly rotund norm and such that there is no $\Phi:E\to c_0(\Gamma )$, for any set $\Gamma$, linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space $E$ is actually the dual space $Y^*$ of a space $Y$ which is a subspace of a WCG space.
Classification : 03E05, 46B20, 46B26
Keywords: WCG Banach space; weakly uniformly rotund norms; tree 
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Argyros, S. A.; Mercourakis, S. A note on the structure of WUR Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 399-408. http://geodesic.mathdoc.fr/item/CMUC_2005__46_3_a2/