Aspects of spectral theory for algebras of measurable operators

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dc.contributor.advisorConradie, JJen_ZA
dc.contributor.authorTembo, Isaac Danielen_ZA
dc.date.accessioned2014-07-31T08:11:00Z
dc.date.available2014-07-31T08:11:00Z
dc.date.issued2008en_ZA
dc.descriptionIncludes abstract.
dc.descriptionIncludes bibliographical references (p. 124-129).
dc.description.abstractThe spectral theory for bounded normal operators on a Hilbert space and the various functional calculi for such operators is closely related to the representation theory of commutative C*- and von Neumann algebras as algebras of bounded continuous or measurable functions. For unbounded operators the corresponding theory leads to algebras of unbounded densely defined operators. The thesis looks at aspects of spectral theory in the non-commutative generalisations of these algebras. Given a von Neumann algebra M, there are various notions of measurability for operators affiliated with M, and the measurable operators of a particular kind form an involutive algebra under the strong sum and product. Algebras of this kind can usually be equipped with a topology modelled on the topology of convergence in measure under which they become topological algebras. The emphasis in this thesis is on a semifinite von Neumann algebra M equipped with a semi-finite faithful normal trace τ and the corresponding algebra M~ of τ-measurable operators.en_ZA
dc.identifier.apacitationTembo, I. D. (2008). <i>Aspects of spectral theory for algebras of measurable operators</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/4934en_ZA
dc.identifier.chicagocitationTembo, Isaac Daniel. <i>"Aspects of spectral theory for algebras of measurable operators."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2008. http://hdl.handle.net/11427/4934en_ZA
dc.identifier.citationTembo, I. 2008. Aspects of spectral theory for algebras of measurable operators. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Tembo, Isaac Daniel AB - The spectral theory for bounded normal operators on a Hilbert space and the various functional calculi for such operators is closely related to the representation theory of commutative C*- and von Neumann algebras as algebras of bounded continuous or measurable functions. For unbounded operators the corresponding theory leads to algebras of unbounded densely defined operators. The thesis looks at aspects of spectral theory in the non-commutative generalisations of these algebras. Given a von Neumann algebra M, there are various notions of measurability for operators affiliated with M, and the measurable operators of a particular kind form an involutive algebra under the strong sum and product. Algebras of this kind can usually be equipped with a topology modelled on the topology of convergence in measure under which they become topological algebras. The emphasis in this thesis is on a semifinite von Neumann algebra M equipped with a semi-finite faithful normal trace τ and the corresponding algebra M~ of τ-measurable operators. DA - 2008 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2008 T1 - Aspects of spectral theory for algebras of measurable operators TI - Aspects of spectral theory for algebras of measurable operators UR - http://hdl.handle.net/11427/4934 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/4934
dc.identifier.vancouvercitationTembo ID. Aspects of spectral theory for algebras of measurable operators. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2008 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/4934en_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.otherMathematics and Applied Mathematicsen_ZA
dc.titleAspects of spectral theory for algebras of measurable operatorsen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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