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arXiv · 1807.03814

Lipschitz free spaces on finite metric spaces

Stephen J. Dilworth·Denka Kutzarova·Mikhail I. Ostrovskii
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Abstract

Main results of the paper: (1) For any finite metric space $M$ the Lipschitz free space on $M$ contains a large well-complemented subspace which 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 graphs which 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.

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Stephen J. Dilworth, Denka Kutzarova, Mikhail I. Ostrovskii. 2018-07-10. Lipschitz free spaces on finite metric spaces. https://arxiv.org/abs/1807.03814

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