“…Given a Banach space \(\mathcal X\), let \(x\) be a point in
ball\((\mathcal X)\), the closed unit
ball of \(\mathcal X\).
We say that \(x\) is a strongly extreme point of
ball\((\mathcal X)\) if it has the following property: for every \(\varepsilon>0\) there is \(\delta>0\) such that the inequalities \(\|x\pm y\|<1+\delta\) imply, for \(y\in\mathcal X\), that \(\|y\|<\varepsilon\). …”
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