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arXiv · 2609.31542

Quotients of $L_1$ by subsequences of the Haar system have cotype 2

Stephen Dilworth·Denka Kutzarova·Mikhail Ostrovskii·Thomas Speckhofer
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Abstract

Let $Y$ be the closed linear span of a subsequence of the Haar system in $L_1$. We prove that the quotient space $L_1/Y$ has cotype~$2$. This result implies that transportation cost spaces on diamond graphs have cotype $2$.

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Stephen Dilworth, Denka Kutzarova, Mikhail Ostrovskii, Thomas Speckhofer. 2026-09-25. Quotients of $L_1$ by subsequences of the Haar system have cotype 2. https://arxiv.org/abs/2609.31542

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