Weakly almost square Lipschitz-free spaces

2022/10/17 by Kaasik, Jaan Kristjan, Veeorg, Triinu
#46B04 (Primary) 46B20 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.09158

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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