Lipschitz-free Spaces on Finite Metric Spaces

Stephen J. Dilworth, Denka Kutzarova, Mikhail I. Ostrovskii

Research output: Contribution to journalArticlepeer-review

Abstract

Main results of the paper are as follows: (1) For anyfinite metric space the Lipschitz-free space on contains a large well-complemented subspace that is close to. (2) Lipschitz-free spaces on large classes of recursively defined sequences of graphs are not uniformly isomorphic to 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.

Original languageEnglish (US)
Pages (from-to)774-804
Number of pages31
JournalCanadian Journal of Mathematics
Volume72
Issue number3
DOIs
StatePublished - Jun 1 2020

Keywords

  • Arens-Eells space
  • Kantorovich-Rubinstein distance
  • Laakso graph
  • Lipschitz-free space
  • Wasserstein distance
  • diamond graph
  • earth mover distance
  • recursive family of graphs
  • transportation cost

ASJC Scopus subject areas

  • Mathematics(all)

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