PreprintCC BY 4.0arXiv
Stability of maximal relative projection constants
Abstract
For positive integers n≥ r, let λ(r,n) denote the \emph{maximal relative projection constant} of r-dimensional subspaces of ℓ∞n and λ(r) denote the \emph{maximal absolute projection constant}, respectively. It is known that for any fixed r, λ(r,n) is a non-decreasing sequence with limit λ(r) as n→ ∞. A natural question is whether λ(r,n) stabilizes at λ(r) for some n>r. We prove that for any fixed r, λ(r,n)=λ(r) for every n≥ 2rbinomr+12. This answers a question of Basso. The technique used is of independent interest.
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BibTeX
@misc{kumar2026stability,
title = {{Stability of maximal relative projection constants}},
author = {Hitesh Kumar and Bojan Mohar and Seyed Ahmad Mojallal and Shivaramakrishna Pragada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03200},
eprint = {2609.03200},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03200},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stability of maximal relative projection constants
AU - Hitesh Kumar
AU - Bojan Mohar
AU - Seyed Ahmad Mojallal
AU - Shivaramakrishna Pragada
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03200
UR - https://arxiv.org/abs/2609.03200
AB - For positive integers n≥ r, let λ(r,n) denote the \emph{maximal relative projection constant} of r-dimensional subspaces of ℓ_∞^n and λ(r) denote the \emph{maximal absolute projection constant}, respectively. It is known that for any fixed r, λ(r,n) is a non-decreasing sequence with limit λ(r) as n→ ∞. A natural question is whether λ(r,n) stabilizes at λ(r) for some n>r. We prove that for any fixed r, λ(r,n)=λ(r) for every n≥ 2^rbinomr+12. This answers a question of Basso. The technique used is of independent interest.
ER -