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6
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Accepted
Hahn-Banach smoothness of $Y^{**}$ in $X^{**}$
$Y^{\bot\bot}$ need not be what you call Hahn-Banach smooth [see below] in $X^{\bot\bot}$: Take $X=L_1[0,1]$ and a smooth point of the unit sphere, e.g. $x=1$. Let $Y$ be the linear span of $x$, which …