A characterisation of octahedrality in Lipschitz-free spaces

2016/12/12 by Procházka, Antonín, Zoca, Abraham Rueda
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1612.03808

Abstract

We characterise the octahedrality of Lipschitz-free space norm in terms of a new geometric property of the underlying metric space. We study the metric spaces with and without this property. Quite surprisingly, metric spaces without this property cannot embed isometrically into ℓ₁ and similar Banach spaces.

Related

• Octahedral norms in duals and biduals of Lipschitz-free spaces
• Octahedrality in Lipschitz free Banach spaces
• Nonrough norms in Lipschitz free spaces
• Lipschitz-free spaces and Schur properties
• Free spaces over some proper metric spaces