Gleason solutions and canonical models for row contractions

dc.contributor.advisorMartin, Robert T Wen_ZA
dc.contributor.authorRamanantoanina, Andriamanankasinaen_ZA
dc.date.accessioned2017-10-03T14:10:27Z
dc.date.available2017-10-03T14:10:27Z
dc.date.issued2017en_ZA
dc.description.abstractThis thesis extends the deBranges-Rovnyak model for completely non-coisometric (CNC) contractions to the setting of row contractions from several copies of a Hilbert space into itself. It is shown that a large class of of row contractions (including all CNC row contractions with commuting components) can be represented as extremal Gleason solutions in the de Branges-Rovnyak space associated to a contractive multiplier between vector-valued Drury-Arveson spaces. Here, a Gleason solution is the appropriate several-variable analogue of the adjoint of the restricted backward shift. Given such a row contraction T, the corresponding multiplier bT , that is, the characteristic function of T, is shown to be unitary invariant. We further characterise a natural sub-class of row contractions for which it is a complete unitary invariant.en_ZA
dc.identifier.apacitationRamanantoanina, A. (2017). <i>Gleason solutions and canonical models for row contractions</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/25491en_ZA
dc.identifier.chicagocitationRamanantoanina, Andriamanankasina. <i>"Gleason solutions and canonical models for row contractions."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017. http://hdl.handle.net/11427/25491en_ZA
dc.identifier.citationRamanantoanina, A. 2017. Gleason solutions and canonical models for row contractions. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Ramanantoanina, Andriamanankasina AB - This thesis extends the deBranges-Rovnyak model for completely non-coisometric (CNC) contractions to the setting of row contractions from several copies of a Hilbert space into itself. It is shown that a large class of of row contractions (including all CNC row contractions with commuting components) can be represented as extremal Gleason solutions in the de Branges-Rovnyak space associated to a contractive multiplier between vector-valued Drury-Arveson spaces. Here, a Gleason solution is the appropriate several-variable analogue of the adjoint of the restricted backward shift. Given such a row contraction T, the corresponding multiplier bT , that is, the characteristic function of T, is shown to be unitary invariant. We further characterise a natural sub-class of row contractions for which it is a complete unitary invariant. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Gleason solutions and canonical models for row contractions TI - Gleason solutions and canonical models for row contractions UR - http://hdl.handle.net/11427/25491 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/25491
dc.identifier.vancouvercitationRamanantoanina A. Gleason solutions and canonical models for row contractions. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/25491en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleGleason solutions and canonical models for row contractionsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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