Weakly almost square Lipschitz-free spaces

Jaan Kristjan Kaasik; Triinu Veeorg

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arXiv · 2210.09158

Weakly almost square Lipschitz-free spaces

Jaan Kristjan Kaasik·Triinu Veeorg

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Abstract

We construct a Lipschitz-free space that is locally almost square but not weakly almost square; this is the first example of such a Banach space. We also prove a result, which indicates that geodesic metric spaces are a potential metric characterization for weakly almost square Lipschitz-free spaces. Lastly, we prove that a Lipschitz-free space can not have the symmetric strong diameter $2$ property.

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Jaan Kristjan Kaasik, Triinu Veeorg. 2022-10-17. Weakly almost square Lipschitz-free spaces. https://arxiv.org/abs/2210.09158

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