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arXiv · 2008.03163

On the duality of the symmetric strong diameter $2$ property in Lipschitz spaces

Andre Ostrak
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Abstract

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.

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Andre Ostrak. 2020-08-07. On the duality of the symmetric strong diameter $2$ property in Lipschitz spaces. https://arxiv.org/abs/2008.03163

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