Isometric Structure of Transportation Cost Spaces on Finite Metric Spaces

dc.authorid Ostrovskii, Mikhail/0000-0002-7164-196X
dc.authorscopusid 35610828900
dc.authorscopusid 7006870450
dc.contributor.author Ostrovska, Sofiya
dc.contributor.author Ostrovskii, Mikhail, I
dc.contributor.other Mathematics
dc.date.accessioned 2024-07-05T15:24:53Z
dc.date.available 2024-07-05T15:24:53Z
dc.date.issued 2022
dc.department Atılım University en_US
dc.department-temp [Ostrovska, Sofiya] Atilim Univ, Dept Math, TR-06830 Ankara, Turkey; [Ostrovskii, Mikhail, I] St Johns Univ, Dept Math & Comp Sci, 8000 Utopia Pkwy, Queens, NY 11439 USA en_US
dc.description Ostrovskii, Mikhail/0000-0002-7164-196X en_US
dc.description.abstract The paper is devoted to isometric Banach-space- theoretical structure of transportation cost (TC) spaces on finite metric spaces. The TC spaces arc also known as Arens-Eells, Lipschitzfree, or Wasserstein spaces. A new notion of a roadmap pertinent to a transportation problem on a finite metric space has been introduced and used to simplify proofs for the results on representation of TC spaces as quotients of l(1) spaces on the edge set over the cycle space. A Tolstoi-type theorem for roadmaps is proved, and directed subgraphs of the canonical graphs, which are supports of maximal optimal roadmaps, are characterized. Possible obstacles for a TC space on a finite metric space X preventing them from containing subspaces isometric to l(infinity)(n) have been found in terms of the canonical graph of X. The fact that TC spaces on diamond graphs do not contain l(infinity)(4) isometrically has been derived. In addition, a short overview of known results on the isometric structure of TC spaces on finite metric spaces is presented. en_US
dc.description.sponsorship Atilim University; National Science Foundation [NSF DMS-1953773] en_US
dc.description.sponsorship The first-named author gratefully acknowledges the support by Atilim University. This paper was written while the first-named author was on research leave supported by Atilim University. The second-named author gratefully acknowledges the support by the National Science Foundation grant NSF DMS-1953773. The authors express their sincere gratitude to the anonymous referee for the useful suggestions and important pointers to the literature. en_US
dc.identifier.citationcount 1
dc.identifier.doi 10.1007/s13398-022-01301-w
dc.identifier.issn 1578-7303
dc.identifier.issn 1579-1505
dc.identifier.issue 4 en_US
dc.identifier.scopus 2-s2.0-85134539930
dc.identifier.scopusquality Q1
dc.identifier.uri https://doi.org/10.1007/s13398-022-01301-w
dc.identifier.uri https://hdl.handle.net/20.500.14411/2462
dc.identifier.volume 116 en_US
dc.identifier.wos WOS:000828107700001
dc.identifier.wosquality Q1
dc.institutionauthor Ostrovska, Sofiya
dc.language.iso en en_US
dc.publisher Springer-verlag Italia Srl en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/openAccess en_US
dc.scopus.citedbyCount 1
dc.subject [No Keyword Available] en_US
dc.title Isometric Structure of Transportation Cost Spaces on Finite Metric Spaces en_US
dc.type Article en_US
dc.wos.citedbyCount 1
dspace.entity.type Publication
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