Year: 2026
Type: preprint
Abstract: We construct a quasi-Banach function lattice $X$ on $\mathbb R$ whose quasi-norm is order continuous and invariant under every translation. Nevertheless, $X$ contains a bounded sequence with common compact support which is equicontinuous in $X$ and has no norm-convergent subsequence. This provides a counterexample to Conjectures 2.5 and 2.11 proposed by Brudnyi in \cite{Brudnyi2015}.
Source: arXiv (Cornell University)
Authors: Huang, Jinghao, Xu, Ran
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221112924