Geodesic
Lipschitz-free Spaces on Finite Metric Spaces
Canadian journal of mathematics, Tome 72 (2020) no. 3, pp. 774-804

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DOI

Main results of the paper are as follows:(1) For any finite metric space $M$ the Lipschitz-free space on $M$ contains a large well-complemented subspace that is close to $\ell _{1}^{n}$.(2) Lipschitz-free spaces on large classes of recursively defined sequences of graphs are not uniformly isomorphic to $\ell _{1}^{n}$ of the corresponding dimensions. These classes contain well-known families of diamond graphs and Laakso graphs.Interesting features of our approach are: (a) We consider averages over groups of cycle-preserving bijections of edge sets of graphs that are not necessarily graph automorphisms. (b) In the case of such recursive families of graphs as Laakso graphs, we use the well-known approach of Grünbaum (1960) and Rudin (1962) for estimating projection constants in the case where invariant projections are not unique.
DOI : 10.4153/S0008414X19000087
Mots-clés : Arens–Eells space, diamond graph, earth mover distance, Kantorovich–Rubinstein distance, Laakso graph, Lipschitz-free space, recursive family of graphs, transportation cost, Wasserstein distance 
Dilworth, Stephen J.; Kutzarova, Denka; Ostrovskii, Mikhail I. Lipschitz-free Spaces on Finite Metric Spaces. Canadian journal of mathematics, Tome 72 (2020) no. 3, pp. 774-804. doi: 10.4153/S0008414X19000087
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     title = {Lipschitz-free {Spaces} on {Finite} {Metric} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {774--804},
     year = {2020},
     volume = {72},
     number = {3},
     doi = {10.4153/S0008414X19000087},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000087/}
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