{"title":"希尔伯特空间中无界可闭算子的海尔-乌兰稳定性","authors":"Arup Majumdar, P. Sam Johnson, Ram N. Mohapatra","doi":"10.1002/mana.202300484","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with some examples. We also present results pertaining to the Hyers–Ulam stability of the sum and product of closable operators to have the Hyers–Ulam stability and the necessary and sufficient conditions of the Schur complement and the quadratic complement of <span></span><math>\n <semantics>\n <mrow>\n <mn>2</mn>\n <mo>×</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$2 \\times 2$</annotation>\n </semantics></math> block matrix <span></span><math>\n <semantics>\n <mi>A</mi>\n <annotation>$\\mathcal {A}$</annotation>\n </semantics></math> in order to have the Hyers–Ulam stability.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hyers–Ulam stability of unbounded closable operators in Hilbert spaces\",\"authors\":\"Arup Majumdar, P. Sam Johnson, Ram N. Mohapatra\",\"doi\":\"10.1002/mana.202300484\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with some examples. We also present results pertaining to the Hyers–Ulam stability of the sum and product of closable operators to have the Hyers–Ulam stability and the necessary and sufficient conditions of the Schur complement and the quadratic complement of <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>2</mn>\\n <mo>×</mo>\\n <mn>2</mn>\\n </mrow>\\n <annotation>$2 \\\\times 2$</annotation>\\n </semantics></math> block matrix <span></span><math>\\n <semantics>\\n <mi>A</mi>\\n <annotation>$\\\\mathcal {A}$</annotation>\\n </semantics></math> in order to have the Hyers–Ulam stability.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300484\",\"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.202300484","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hyers–Ulam stability of unbounded closable operators in Hilbert spaces
In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with some examples. We also present results pertaining to the Hyers–Ulam stability of the sum and product of closable operators to have the Hyers–Ulam stability and the necessary and sufficient conditions of the Schur complement and the quadratic complement of block matrix in order to have the Hyers–Ulam stability.
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