{"title":"Extensions of symmetric operators I: The inner characteristic function case","authors":"R.T.W. Martin","doi":"10.1515/conop-2015-0004","DOIUrl":null,"url":null,"abstract":"Abstract Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2014-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2015-0004","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2015-0004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 6
Abstract
Abstract Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.