{"title":"格尔斯戈林圆定理的希尔伯特空间变体","authors":"Marcus Carlsson, Olof Rubin","doi":"10.1002/mana.202300153","DOIUrl":null,"url":null,"abstract":"<p>We provide a variant of Geršgorin's circle theorem, where the <span></span><math>\n <semantics>\n <msup>\n <mi>ℓ</mi>\n <mn>1</mn>\n </msup>\n <annotation>$\\ell ^1$</annotation>\n </semantics></math>-estimates are swapped for <span></span><math>\n <semantics>\n <msup>\n <mi>ℓ</mi>\n <mn>2</mn>\n </msup>\n <annotation>$\\ell ^2$</annotation>\n </semantics></math>-estimates, more suitable for the infinite-dimensional Hilbert space setting.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300153","citationCount":"0","resultStr":"{\"title\":\"A Hilbert-space variant of Geršgorin's circle theorem\",\"authors\":\"Marcus Carlsson, Olof Rubin\",\"doi\":\"10.1002/mana.202300153\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We provide a variant of Geršgorin's circle theorem, where the <span></span><math>\\n <semantics>\\n <msup>\\n <mi>ℓ</mi>\\n <mn>1</mn>\\n </msup>\\n <annotation>$\\\\ell ^1$</annotation>\\n </semantics></math>-estimates are swapped for <span></span><math>\\n <semantics>\\n <msup>\\n <mi>ℓ</mi>\\n <mn>2</mn>\\n </msup>\\n <annotation>$\\\\ell ^2$</annotation>\\n </semantics></math>-estimates, more suitable for the infinite-dimensional Hilbert space setting.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300153\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300153\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300153","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Hilbert-space variant of Geršgorin's circle theorem
We provide a variant of Geršgorin's circle theorem, where the -estimates are swapped for -estimates, more suitable for the infinite-dimensional Hilbert space setting.