{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/4934"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/4934","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Aspects of spectral theory for algebras of measurable operators","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Tembo, Isaac Daniel"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Conradie, JJ"],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008","date_published":"2008","updated_at":"2026-07-22T22:23:04Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/4934","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Conradie, JJ"]},{"key":"dc:creator","label":"Author","values":["Tembo, Isaac Daniel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-07-31T08:11:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-07-31T08:11:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2008"]},{"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":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"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/11427/4934"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes abstract.","Includes bibliographical references (p. 124-129)."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Aspects of spectral theory for algebras of measurable operators"]}]}],"canonical_facts":{"dc:contributor.advisor":["Conradie, JJ"],"dc:creator":["Tembo, Isaac Daniel"],"dc:date.accessioned":["2014-07-31T08:11:00Z"],"dc:date.available":["2014-07-31T08:11:00Z"],"dc:date.issued":["2008"],"dc:description":["Includes abstract.","Includes bibliographical references (p. 124-129)."],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/4934"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Aspects of spectral theory for algebras of measurable operators"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:23:04Z"}