## 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 language | English (US) |
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Pages (from-to) | 774-804 |

Number of pages | 31 |

Journal | Canadian Journal of Mathematics |

Volume | 72 |

Issue number | 3 |

DOIs | |

State | Published - 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

- General Mathematics