When is a subspace of $\ell_\infty^N$ isometrically isomorphic to $\ell_\infty^n$?
Functional Analysis
2025-09-23 v1
Abstract
It is shown in this note that one can decide whether an -dimensional subspace of is isometrically isomorphic to by testing a finite number of determinental inequalities. As a byproduct, an elementary proof is provided for the fact that an -dimensional subspace of with projection constant equal to one must be isometrically isomorphic to .
Keywords
Cite
@article{arxiv.2509.16807,
title = {When is a subspace of $\ell_\infty^N$ isometrically isomorphic to $\ell_\infty^n$?},
author = {Beata Deregowska and Simon Foucart and Barbara Lewandowska},
journal= {arXiv preprint arXiv:2509.16807},
year = {2025}
}