The local diameter two property and the diameter two property in spaces of Lipschitz functions

2025/01/17 by R. Haller, Haller, Rainis, Jaan Kristjan Kaasik +3 · 1 citation
Computer Science · Mathematics · #46B04 (Primary) #46B20 (Secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2501.10082

openalex publication_date 2025/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We separate the local diameter two property from the diameter two property and their weak-star counterparts from each other in spaces of Lipschitz functions. We characterise the w^*-LD2P, the w^*-D2P, the LD2P, and the SD2P in these spaces. We introduce a generalised version of cyclical monotonicity to study functionals on spaces of Lipschitz functions.

Cited by

• On Weak Compactness and Uniform Regularity in Lipschitz free Spaces

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