Year: 2026
Type: preprint
Abstract: We construct an explicit symmetric Banach norm on a function space over $(0,\infty)$ which is monotone with respect to logarithmic submajorization but is not strongly symmetric, and hence is not fully symmetric. This answers a question raised by Dodds, Dodds, Sukochev, and Zanin. We also construct a strongly symmetric Banach function space over $(0,\infty)$ which is monotone with respect to logarithmic submajorization and admits no equivalent fully symmetric norm.
Source: arXiv (Cornell University)
Author: Huang, Jinghao
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213612353