{"title":"Schatten classes on noncommutative tori: Kernel conditions","authors":"M. Ruzhansky, K. Zeng","doi":"arxiv-2407.09715","DOIUrl":null,"url":null,"abstract":"In this note, we give criteria on noncommutative integral kernels ensuring\nthat integral operators on quantum torus belong to Schatten classes. With the\nengagement of a noncommutative Schwartz' kernel theorem on the quantum torus, a\nspecific test for Schatten class properties of bounded operators on the quantum\ntorus is established.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.09715","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we give criteria on noncommutative integral kernels ensuring
that integral operators on quantum torus belong to Schatten classes. With the
engagement of a noncommutative Schwartz' kernel theorem on the quantum torus, a
specific test for Schatten class properties of bounded operators on the quantum
torus is established.
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