{"title":"Inequalities between s-numbers","authors":"Mario Ullrich","doi":"10.1007/s43036-024-00386-x","DOIUrl":null,"url":null,"abstract":"<div><p>Singular numbers of linear operators between Hilbert spaces were generalized to Banach spaces by s-numbers (in the sense of Pietsch). This allows for different choices, including approximation, Gelfand, Kolmogorov and Bernstein numbers. Here, we present an elementary proof of a bound between the smallest and the largest s-number.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00386-x.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00386-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Singular numbers of linear operators between Hilbert spaces were generalized to Banach spaces by s-numbers (in the sense of Pietsch). This allows for different choices, including approximation, Gelfand, Kolmogorov and Bernstein numbers. Here, we present an elementary proof of a bound between the smallest and the largest s-number.
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