Representation of non-commutative topological algebras

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dc.contributor.advisorKotzé, Wen_ZA
dc.contributor.authorHacking, Susan Margareten_ZA
dc.date.accessioned2016-10-25T13:35:09Z
dc.date.available2016-10-25T13:35:09Z
dc.date.issued1970en_ZA
dc.description.abstractThe 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.en_ZA
dc.identifier.apacitationHacking, S. M. (1970). <i>Representation of non-commutative topological algebras</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/22297en_ZA
dc.identifier.chicagocitationHacking, Susan Margaret. <i>"Representation of non-commutative topological algebras."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1970. http://hdl.handle.net/11427/22297en_ZA
dc.identifier.citationHacking, S. 1970. Representation of non-commutative topological algebras. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Hacking, Susan Margaret AB - 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. DA - 1970 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1970 T1 - Representation of non-commutative topological algebras TI - Representation of non-commutative topological algebras UR - http://hdl.handle.net/11427/22297 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/22297
dc.identifier.vancouvercitationHacking SM. Representation of non-commutative topological algebras. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1970 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/22297en_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.titleRepresentation of non-commutative topological algebrasen_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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