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<p>We prove a weak version of the <i>ε</i>-Dvoretzky conjecture for normed spaces, showing the existence of a subspace of ℝ<sup><i>n</i></sup> of dimension at least <i>c</i> log <i>n</i>/∣ log <i>ε</i>∣ in which the given norm is <i>ε</i>-close to a norm obeying a large discrete group of symmetries (“1-unconditional norm”).</p>

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A weak version of the ε-Dvoretzky conjecture for normed spaces

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  • 发表日期：

    2026年4月6日

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  • Bo’az Klartag,
  • Tomer Novikov

摘要

We prove a weak version of the ε-Dvoretzky conjecture for normed spaces, showing the existence of a subspace of ℝn of dimension at least c log n/∣ log ε∣ in which the given norm is ε-close to a norm obeying a large discrete group of symmetries (“1-unconditional norm”).