Year: 2021
Type: preprint
Abstract: Ball's complex plank theorem states that if $v_1,\dots,v_n$ are unit vectors in $\mathbb{C}^d$, and $t_1,\dots,t_n$, non-negative numbers satisfying $\sum_{k=1}^nt_k^2 = 1,$ then there exists a unit vector $v$ in $\mathbb{C}^d$ for which $|\langle v_k,v \rangle | \geq t_k$ for every $k$. Here we present a streamlined version of Ball's original proof.
Source: arXiv (Cornell University)
Author: Ortega-Moreno, Oscar
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W4226517231