A logarithmically monotone symmetric norm which is not fully symmetric

作者： Jinghao Huang ¹
作者单位：

1. Harbin Insitute of technology
通讯作者： Jinghao Huang Email:jinghao.huang@hit.edu.cn
提交时间：2026-09-06 06:01:04

摘要: 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.

Symmetric Banach function space logarithmic submajorization Hardy--Littlewood submajorization Marcinkiewicz space

来自： 黄景灏
分类： 数学 >> 数学（综合）
投稿状态： 已投稿期刊
引用： ChinaXiv:202609.00459 (或此版本 ChinaXiv:202609.00459V1)
DOI:10.12074/202609.00459
CSTR:32003.36.ChinaXiv.202609.00459
科创链TXID： 2a1be904-7c71-4977-9d90-44f2da6f072f
推荐引用方式： Jinghao Huang.A logarithmically monotone symmetric norm which is not fully symmetric.中国科学院科技论文预发布平台.[DOI:10.12074/202609.00459] (点此复制)

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2026-09-06 06:01:04

ChinaXiv:202609.00459V1

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2. Tingley&amp;#039;s Problem for Schatten \(p\)-Classes, $0&amp;lt;p\ne 2&amp;lt;\infty$	2026-09-06
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A logarithmically monotone symmetric norm which is not fully symmetric

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