The study shows the existence of an ε-close subspace norm in normed spaces, suggesting significant implications for mathematical theory.
We prove a weak version of the ε -Dvoretzky conjecture for normed spaces, showing the existence of a subspace of ℝ n 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”).
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Klartag et al. (2026) studied this question.