When is a subspace of ℓ_∞^N isometrically isomorphic to ℓ_∞ⁿ?

2025/09/20 by Beata Derȩgowska, Deregowska, Beata, Simon Foucart +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2509.16807

openalex publication_date 2025/09/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

It is shown in this note that one can decide whether an n-dimensional subspace of ℓ_∞^N is isometrically isomorphic to ℓ_∞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 ℓ_∞^N with projection constant equal to one must be isometrically isomorphic to ℓ_∞ⁿ.

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