Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property

2022/06/10 by R. Jeffrey Smith, Smith, Richard J., Filip Talimdjioski +1 · 1 citation
Mathematics · #46B20 #46B28 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2206.04953

openalex publication_date 2022/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ‖⋅‖ be a norm on ℝ^N and let M be a closed C¹-submanifold of ℝ^N. Consider the pointed metric space (M,d), where d is the metric given by d(x,y)=‖x-y‖, x,y∈ M. Then the Lipschitz-free space F(M) has the Metric Approximation Property.

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• Lipschitz-free spaces and Bossard's reduction argument

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