{"title":"关于部分等距的高-王-吴猜想在5乘5情况下成立","authors":"I. Spitkovsky, I. Suleiman, E. Wegert","doi":"10.13001/ela.2022.6541","DOIUrl":null,"url":null,"abstract":"Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for $n\\leq 4$) that an $n$-by-$n$ partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds for $n=5$.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Gau-Wang-Wu conjecture on partial isometries holds in the 5-by-5 case\",\"authors\":\"I. Spitkovsky, I. Suleiman, E. Wegert\",\"doi\":\"10.13001/ela.2022.6541\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for $n\\\\leq 4$) that an $n$-by-$n$ partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds for $n=5$.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2022.6541\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2022.6541","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
The Gau-Wang-Wu conjecture on partial isometries holds in the 5-by-5 case
Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for $n\leq 4$) that an $n$-by-$n$ partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds for $n=5$.
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