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Representation of non-commutative topological algebras
The well known Gelfland-Naimark theorem enables us to represent a complex commutative C*-algebra as a full algebra of complex valued functions defined on its set of primitive ideals which is called the structure space of the algebra. In is thesis we are concerned with the generalization of this type...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867614318402469888 |
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| access_status_str | Open Access |
| author | Hacking, Susan Margaret |
| author2 | Kotzé, W |
| author_browse | Hacking, Susan Margaret Kotzé, W |
| author_facet | Kotzé, W Hacking, Susan Margaret |
| author_sort | Hacking, Susan Margaret |
| collection | Thesis |
| description | The well known Gelfland-Naimark theorem enables us to represent a complex commutative C*-algebra as a full algebra of complex valued functions defined on its set of primitive ideals which is called the structure space of the algebra. In is thesis we are concerned with the generalization of this type of representation theorem to non-commutative rings and algebras. In order to prove the Gelfand-Naimark theorem, we needed the Stone-Weierstrass theorem to enable us to show that a subalgebra is actually equal to a full algebra of functions. We shall see that in order to represent a non-commutative algebra as a set of functions taking values in a variable range, we shall need a suitable type of Stone-Weierstrass theorem. This thesis can therefore be considered as an illustration of the application of Stone-Weierstrass type argunents to the theory of C*-algebra representations. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/22297 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:50:08.413Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| 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:11427/22297 Representation of non-commutative topological algebras Hacking, Susan Margaret Kotzé, W Mathematics The well known Gelfland-Naimark theorem enables us to represent a complex commutative C*-algebra as a full algebra of complex valued functions defined on its set of primitive ideals which is called the structure space of the algebra. In is thesis we are concerned with the generalization of this type of representation theorem to non-commutative rings and algebras. In order to prove the Gelfand-Naimark theorem, we needed the Stone-Weierstrass theorem to enable us to show that a subalgebra is actually equal to a full algebra of functions. We shall see that in order to represent a non-commutative algebra as a set of functions taking values in a variable range, we shall need a suitable type of Stone-Weierstrass theorem. This thesis can therefore be considered as an illustration of the application of Stone-Weierstrass type argunents to the theory of C*-algebra representations. 2016-10-25T13:35:09Z 2016-10-25T13:35:09Z 1970 Master Thesis Masters MSc http://hdl.handle.net/11427/22297 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Hacking, Susan Margaret Representation of non-commutative topological algebras |
| thesis_degree_str | Master's |
| title | Representation of non-commutative topological algebras |
| title_full | Representation of non-commutative topological algebras |
| title_fullStr | Representation of non-commutative topological algebras |
| title_full_unstemmed | Representation of non-commutative topological algebras |
| title_short | Representation of non-commutative topological algebras |
| title_sort | representation of non commutative topological algebras |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/22297 |
| work_keys_str_mv | AT hackingsusanmargaret representationofnoncommutativetopologicalalgebras |