{"title":"正规算子的分解及其在谱定理中的应用","authors":"Katsukuni Nakagawa","doi":"10.17654/FA012010037","DOIUrl":null,"url":null,"abstract":"A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"DECOMPOSITION OF NORMAL OPERATORS AND ITS APPLICATION TO SPECTRAL THEOREM\",\"authors\":\"Katsukuni Nakagawa\",\"doi\":\"10.17654/FA012010037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.\",\"PeriodicalId\":8426,\"journal\":{\"name\":\"arXiv: Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17654/FA012010037\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/FA012010037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
DECOMPOSITION OF NORMAL OPERATORS AND ITS APPLICATION TO SPECTRAL THEOREM
A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.
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