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arXiv · 2206.13273

A weak version of the $\varepsilon$-Dvoretzky conjecture for normed spaces

Bo'az Klartag·Tomer Novikov
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Abstract

We prove a weak version of the $\varepsilon$-Dvoretzky conjecture for normed spaces, showing the existence of a subspace of $\mathbb{R}^n$ of dimension at least $c \log n / |\log \varepsilon|$ in which the given norm is $\varepsilon$-close to a norm obeying a large discrete group of symmetries ("$1$-unconditional norm").

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Bo'az Klartag, Tomer Novikov. 2022-06-27. A weak version of the $\varepsilon$-Dvoretzky conjecture for normed spaces. https://arxiv.org/abs/2206.13273

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