We characterise the weak\(^*\) symmetric strong diameter 2 property in Lipschitz function spaces by a property of its predual, the Lipschitz-free space. We call this new property decomposable octahedrality and study its duality with the symmetric strong diameter 2 property in general. For a Banach space to be decomposably octahedral it is sufficient that its dual space has the weak\(^*\) symmetric strong diameter 2 property. Whether it is also a necessary condition remains open.

中文翻译：

---

Lipschitz空间中对称强直径2性质的对偶性

我们通过其先验的无Lipschitz空间描述了Lipschitz函数空间中的弱\（^ * \）对称强直径2性质。我们称这种新特性为可分解的八面体，并通常以对称的强直径2特性来研究其对偶性。要使Banach空间可分解为八面体，其对偶空间具有弱的\（^ * \）对称强直径2性质就足够了。是否也是必要条件仍待定。