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A logarithmically monotone symmetric norm which is not fully symmetric
Abstract
We construct an explicit symmetric Banach norm on a function space over (0,∞) 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,∞) which is monotone with respect to logarithmic submajorization and admits no equivalent fully symmetric norm.
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BibTeX
@misc{huang2026logarithmically,
title = {{A logarithmically monotone symmetric norm which is not fully symmetric}},
author = {Jinghao Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20270},
eprint = {2609.20270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20270},
}
RIS
TY - UNPB
TI - A logarithmically monotone symmetric norm which is not fully symmetric
AU - Jinghao Huang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20270
UR - https://arxiv.org/abs/2609.20270
AB - We construct an explicit symmetric Banach norm on a function space over (0,∞) 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,∞) which is monotone with respect to logarithmic submajorization and admits no equivalent fully symmetric norm.
ER -