J. Huang , Y. Nessipbayev , F. Sukochev , D. Zanin
{"title":"Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus","authors":"J. Huang , Y. Nessipbayev , F. Sukochev , D. Zanin","doi":"10.1016/j.jfa.2025.110946","DOIUrl":null,"url":null,"abstract":"<div><div>We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the commutative setting; while the second resembles the Kolmogorov–Riesz compactness theorem (see <span><span>Theorem 4.1</span></span>, <span><span>Theorem 5.7</span></span>, respectively). The work contributes to understanding a conjecture of Brudnyi, adapted here for the non-commutative torus.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110946"},"PeriodicalIF":1.7000,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123625001284","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the commutative setting; while the second resembles the Kolmogorov–Riesz compactness theorem (see Theorem 4.1, Theorem 5.7, respectively). The work contributes to understanding a conjecture of Brudnyi, adapted here for the non-commutative torus.
期刊介绍:
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis