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arXiv · 2610.06141

Projection Constants and Banach-Mazur Distance in Codimension Two

Beata Deregowska·Barbara Lewandowska
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Abstract

We prove that every subspace $V\subset\ell_\infty^N$ of codimension one or two with absolute projection constant $λ(V)<4/3$ satisfies $$ d(V,\ell_\infty^{\dim V}) \leq\frac{λ(V)}{4-3λ(V)}. $$ We conjecture that the codimension assumption can be removed and that the same estimate holds for every subspace $V\subset\ell_\infty^N$ with $λ(V)<4/3$.

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Beata Deregowska, Barbara Lewandowska. 2026-10-05. Projection Constants and Banach-Mazur Distance in Codimension Two. https://arxiv.org/abs/2610.06141

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