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arXiv · 1907.01155

Isometric copies of $\ell_\infty^n$ and $\ell_1^n$ in transportation cost spaces on finite metric spaces

Seychelle S. Khan·Mutasim Mim·Mikhail I. Ostrovskii
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Abstract

Main results: (a) If a metric space contains $2n$ elements, the transportation cost space on it contains a $1$-complemented isometric copy of $\ell_1^n$. (b) An example of a finite metric space whose transportation cost space contains an isometric copy of $\ell_\infty^4$. Transportation cost spaces are also known as Arens-Eells, Lipschitz-free, or Wasserstein $1$ spaces.

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Seychelle S. Khan, Mutasim Mim, Mikhail I. Ostrovskii. 2019-07-02. Isometric copies of $\ell_\infty^n$ and $\ell_1^n$ in transportation cost spaces on finite metric spaces. https://doi.org/10.1515/9783110656756-014

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