On relations between transportation cost spaces and l1

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:491

Article

Ostrovska, Sofiya¹  Ostrovskii, Mikhail I.² 

[1] Atilim Univ, Dept Math, TR-06830 Ankara, Turkey

[2] St Johns Univ, Dept Math & Comp Sci, 8000 Utopia Pkwy, Queens, NY 11439 USA

关键词: Arens-Eells space;    Earth mover distance;    Kantorovich-Rubinstein distance;    Lipschitz-free space;    Transportation cost;    Wasserstein distance;   

DOI  :  10.1016/j.jmaa.2020.124338

来源: Elsevier

【 摘 要 】

The present paper deals with some structural properties of transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and Wasserstein spaces. The main results of this work are: (1) A necessary and sufficient condition on an infinite metric space M, under which the transportation cost space on M contains an isometric copy of l(1). The obtained condition is applied to answer the open questions asked by Cuth and Johanis (2017) concerning several specific metric spaces. (2) The description of the transportation cost space of a weighted finite graph G as the quotient l(1) (E(G))/Z(G), where E(G) is the edge set and Z(G) is the cycle space of G. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free