Year: 2026
Type: preprint
Abstract: For positive integers $n\ge r$, let $λ(r,n)$ denote the \emph{maximal relative projection constant} of $r$-dimensional subspaces of $\ell_\infty^n$ 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 $n\to \infty$. A natural question is whether $λ(r,n)$ stabilizes at $λ(r)$ for some $n>r$. We prove that for any fixed $r$, \[λ(r,n)=λ(r) \qquad \text{for every}\qquad n\ge 2^{r}\binom{r+1}{2}.\] This answers a question of Basso. The technique used is of independent interest.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1866363149, G5099342464, G8787022471
OpenAlex ID: W7208790276