{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/25491"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/25491","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Gleason solutions and canonical models for row contractions","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Ramanantoanina, Andriamanankasina"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Martin, Robert T W"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-22T22:22:47Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/25491","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Martin, Robert T W"]},{"key":"dc:creator","label":"Author","values":["Ramanantoanina, Andriamanankasina"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-10-03T14:10:27Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-10-03T14:10:27Z"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/25491"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Gleason solutions and canonical models for row contractions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Martin, Robert T W"],"dc:creator":["Ramanantoanina, Andriamanankasina"],"dc:date.accessioned":["2017-10-03T14:10:27Z"],"dc:date.available":["2017-10-03T14:10:27Z"],"dc:date.issued":["2017"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/25491"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Gleason solutions and canonical models for row contractions"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:47Z"}