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arXiv · 2203.08229

Metric embeddings of Laakso graphs into Banach spaces

S. J. Dilworth·Denka Kutzarova·Svetozar Stankov
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Abstract

Let $X$ be Banach space which is not super-reflexive. Then, for each $n\ge1$ and $\varepsilon>0$, we exhibit metric embeddings of the Laakso graph $\mathcal{L}_n$ into $X$ with distortion less than $2+\varepsilon$ and into $L_1[0,1]$ with distortion $4/3$. The distortion of an embedding of $\mathcal{L}_2$ (respectively, the diamond graph $D_2$) into $L_1[0,1]$ is at least $9/8$ (respectively, $5/4$).

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S. J. Dilworth, Denka Kutzarova, Svetozar Stankov. 2022-03-15. Metric embeddings of Laakso graphs into Banach spaces. https://arxiv.org/abs/2203.08229

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