Isometric structure of transportation cost spaces on finite metric spaces
نویسندگان
چکیده
The paper is devoted to isometric Banach-space-theoretical structure of transportation cost (TC) spaces on finite metric spaces. TC are also known as Arens-Eells, Lipschitz-free, or Wasserstein A new notion a roadmap pertinent problem space has been introduced and used simplify proofs for the results representation quotients $$\ell _1$$ edge set over cycle space. Tolstoi-type theorem roadmaps proved, directed subgraphs canonical graphs, which supports maximal optimal roadmaps, characterized. Possible obstacles X preventing them from containing subspaces _\infty ^n$$ have found in terms graph X. fact that diamond graphs do not contain ^4$$ isometrically derived. In addition, short overview presented.
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ژورنال
عنوان ژورنال: Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas
سال: 2022
ISSN: ['1578-7303', '1579-1505']
DOI: https://doi.org/10.1007/s13398-022-01301-w