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arXiv · 2509.16807

When is a subspace of $\ell_\infty^N$ isometrically isomorphic to $\ell_\infty^n$?

Beata Deregowska·Simon Foucart·Barbara Lewandowska
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Abstract

It is shown in this note that one can decide whether an $n$-dimensional subspace of $\ell_\infty^N$ is isometrically isomorphic to $\ell_\infty^n$ by testing a finite number of determinental inequalities. As a byproduct, an elementary proof is provided for the fact that an $n$-dimensional subspace of $\ell_\infty^N$ with projection constant equal to one must be isometrically isomorphic to $\ell_\infty^n$.

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Beata Deregowska, Simon Foucart, Barbara Lewandowska. 2025-09-20. When is a subspace of $\ell_\infty^N$ isometrically isomorphic to $\ell_\infty^n$?. https://arxiv.org/abs/2509.16807

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