{"title":"线性泛函的极大扩展","authors":"Fabio BURDERİ, Camillo TRAPANI, Salvatore TRİOLO","doi":"10.33205/cma.1310238","DOIUrl":null,"url":null,"abstract":"Extensions of a positive hermitian linear functional $\\omega$, defined on a dense *-subalgebra $\\mathfrak{A_{0}}$ of a topological *-algebra $\\mathfrak{A}[\\tau]$ are analyzed. It turns out that their maximal extension as linear functionals or hermitian linear functional are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [1] is rivisited from this point of view. Examples mostly taken from the theory of integration are discussed.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maximal extensions of a linear functional\",\"authors\":\"Fabio BURDERİ, Camillo TRAPANI, Salvatore TRİOLO\",\"doi\":\"10.33205/cma.1310238\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Extensions of a positive hermitian linear functional $\\\\omega$, defined on a dense *-subalgebra $\\\\mathfrak{A_{0}}$ of a topological *-algebra $\\\\mathfrak{A}[\\\\tau]$ are analyzed. It turns out that their maximal extension as linear functionals or hermitian linear functional are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [1] is rivisited from this point of view. Examples mostly taken from the theory of integration are discussed.\",\"PeriodicalId\":36038,\"journal\":{\"name\":\"Constructive Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Constructive Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33205/cma.1310238\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Constructive Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33205/cma.1310238","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Extensions of a positive hermitian linear functional $\omega$, defined on a dense *-subalgebra $\mathfrak{A_{0}}$ of a topological *-algebra $\mathfrak{A}[\tau]$ are analyzed. It turns out that their maximal extension as linear functionals or hermitian linear functional are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [1] is rivisited from this point of view. Examples mostly taken from the theory of integration are discussed.