Year: 2026
Type: preprint
Abstract: We prove that there exists an absolute constant $c>1$ such that for every $n \geq 3$ there exists an $n$-dimensional real normed space $X$ for which every linear projection $P$ onto a hyperplane satisfies $\|P\| \geq c$. More generally, for every integer $k \geq 1$ there exists a constant $c_k>1$ such that for every $n \geq k+2$ there exists an $n$-dimensional real normed space $X$ such that every projection $P$ onto a subspace of codimension at most $k$ satisfies $\|P\| \geq c_k$. The proof is based on an idea of Gleit and Lazar, who established an analogous result for the space of real $n \times n$ matrices equipped with either the trace-class norm or the operator norm
Source: arXiv (Cornell University)
Author: Kobos, Tomasz
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220930868