PreprintCC BY 4.0arXiv
Projection Constants and Banach-Mazur Distance in Codimension Two
Abstract
We prove that every subspace V⊂ℓ∞N of codimension one or two with absolute projection constant λ(V)<4/3 satisfies d(V,ℓ∞dim V) ≤λ(V)/(4−3λ(V)). We conjecture that the codimension assumption can be removed and that the same estimate holds for every subspace V⊂ℓ∞N with λ(V)<4/3.
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BibTeX
@misc{deregowska2026projection,
title = {{Projection Constants and Banach-Mazur Distance in Codimension Two}},
author = {Beata Deregowska and Barbara Lewandowska},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06141},
eprint = {2610.06141},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06141},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Projection Constants and Banach-Mazur Distance in Codimension Two
AU - Beata Deregowska
AU - Barbara Lewandowska
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06141
UR - https://arxiv.org/abs/2610.06141
AB - We prove that every subspace V⊂ℓ_∞^N of codimension one or two with absolute projection constant λ(V)<4/3 satisfies d(V,ℓ_∞^dim V) ≤λ(V)/(4−3λ(V)). We conjecture that the codimension assumption can be removed and that the same estimate holds for every subspace V⊂ℓ_∞^N with λ(V)<4/3.
ER -