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WCG Banach space; weakly uniformly rotund norms; tree
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.
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