Diameter two properties for spaces of Lipschitz functions

2022/05/26 by R. Haller, Haller, Rainis, Andre Ostrak +3
Computer Science · Mathematics · #46B04 #46B20 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2205.13287

openalex publication_date 2022/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve some open problems regarding diameter two properties within the class of Banach spaces of real-valued Lipschitz functions by using the de Leeuw transform. Namely, we show that: the diameter two property, the strong diameter two property, and the symmetric strong diameter two property are all different for these spaces of Lipschitz functions; the space Lip₀(K_n) has the symmetric strong diameter two property for every n∈ ℕ, including the case of n=2; every local norm-one Lipschitz function is a Daugavet point.

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