article.page.titleprefix On relations between transportation cost spaces and ℓ1
Date
2020-11-15
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of Mathematical Analysis and Applications
Abstract
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 ℓ1.The obtained condition is applied to answer the open questions asked by Cúth 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 ℓ1(E(G))/Z(G), where E(G) is the edge set and Z(G) is the cycle space of G.
Description
Published by Journal of Mathematical Analysis and Applications; https://doi.org/10.1016/j.jmaa.2020.124338; Sofiya Ostrovska, Department of Mathematics, Atilim University, 06830 Incek, Ankara, Turkey; Mikhail I. Ostrovskii, Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Queens, NY 11439, USA.
Keywords
Arens-Eells space; Earth mover distance; Kantorovich-Rubinstein distance; Lipschitz-free space; Transportation cost; Wasserstein distance
Citation
https://hdl.handle.net/20.500.14411/2017