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Gleason solutions and canonical models for row contractions
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...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2017
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| _version_ | 1867613191321681920 |
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| access_status_str | Open Access |
| author | Ramanantoanina, Andriamanankasina |
| author2 | Martin, Robert T W |
| author_browse | Martin, Robert T W Ramanantoanina, Andriamanankasina |
| author_facet | Martin, Robert T W Ramanantoanina, Andriamanankasina |
| author_sort | Ramanantoanina, Andriamanankasina |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/25491 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:13.078Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/25491 Gleason solutions and canonical models for row contractions Ramanantoanina, Andriamanankasina Martin, Robert T W Mathematics 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. 2017-10-03T14:10:27Z 2017-10-03T14:10:27Z 2017 Master Thesis Masters MSc http://hdl.handle.net/11427/25491 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Ramanantoanina, Andriamanankasina Gleason solutions and canonical models for row contractions |
| thesis_degree_str | Master's |
| title | Gleason solutions and canonical models for row contractions |
| title_full | Gleason solutions and canonical models for row contractions |
| title_fullStr | Gleason solutions and canonical models for row contractions |
| title_full_unstemmed | Gleason solutions and canonical models for row contractions |
| title_short | Gleason solutions and canonical models for row contractions |
| title_sort | gleason solutions and canonical models for row contractions |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/25491 |
| work_keys_str_mv | AT ramanantoaninaandriamanankasina gleasonsolutionsandcanonicalmodelsforrowcontractions |