Complementability of isometric copies of ℓ₁ in transportation cost spaces

2022/12/24 by Sofiya Ostrovska, Ostrovska, Sofiya, Mikhail I. Ostrovskii +1
Mathematics · #46B20 #46B85 #6B04 #91B32 #Advanced Banach Space Theory #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2212.12818

openalex publication_date 2022/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work aims to establish new results pertaining to the structure of transportation cost spaces. Due to the fact that those spaces were studied and applied in various contexts, they have also become known under different names such as Arens-Eells spaces, Lipschitz-free spaces, and Wasserstein spaces. The main outcome of this paper states that if a metric space X is such that the transportation cost space on X contains an isometric copy of ℓ₁, then it contains a 1-complemented isometric copy of ℓ₁.

Related

• Isometric structure of transportation cost spaces on finite metric spaces
• Transportation cost spaces and their embeddings into L₁, a Survey
• Dual Banach spaces which contain an isometric copy of L₁
• Bi-Lipschitz embeddings of the space of unordered m-tuples with a partial transportation metric
• Some remarks on the structure of Lipschitz-free spaces