On relations between transportation cost spaces and <i>l</i><sub>1</sub>

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On relations between transportationOstrovskaAtilimJMAA2024.pdf (372.9 KB)

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2020

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Ostrovska, Sofiya
Ostrovskii, Mikhail I.

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Academic Press inc Elsevier Science

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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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 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.

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Arens-Eells space, Earth mover distance, Kantorovich-Rubinstein distance, Lipschitz-free space, Transportation cost, Wasserstein distance

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8

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Q2

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Q2

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Volume

491

Issue

2

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https://doi.org/10.1016/j.jmaa.2020.124338
 https://hdl.handle.net/20.500.14411/3209

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