2 problems

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Polynomial-dimensional embedding conjecture for finite subsets of $\ell_1$
Let $\mathcal{M}\subseteq \ell_1$ be a subset with $|\mathcal{M}|=n$ . An embedding of $\mathcal{M}$ into a normed space has distortion $D$ if distances are preserved up to a multip…
Conjectureopendimensionality-reduction ell-1 metric-embeddingsarXiv posted 2 days ago
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Negative norming-set conjecture for the Banach space $\ell^1$
Let $X=\ell^1$ . For $\lambda\geq 1$ , say that $\lambda$ satisfies Proposition A(i) for $X$ if there exists a weak-compact $\lambda$ -norming subset $K$ of $\operatorname{Ba} X^*$ su…
Conjectureopenbanach-spaces ell-1 functional-analysisarXiv posted 2 days ago

Polynomial-dimensional embedding conjecture for finite subsets of ℓ1\ell_1ℓ1​