{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/25167"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/25167","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Isometries on symmetric spaces associated with semi-finite von Neumann algebras","abstract":"Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be considered a non-commutative composition operator) weighted by a partial isometry and/or a positive operator. In this thesis we describe the structures of isometries on various (non-commutative) symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing characterizations of extreme points in a certain class of Lorentz spaces and in various types of Orlicz spaces.","abstract_html":"Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be considered a non-commutative composition operator) weighted by a partial isometry and/or a positive operator. In this thesis we describe the structures of isometries on various (non-commutative) symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing characterizations of extreme points in a certain class of Lorentz spaces and in various types of Orlicz spaces.","abstract_has_math":false,"creators":["De Jager, Pierre"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Conradie, Jurie J","Martin, R T W"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-22T22:23:05Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/25167","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Conradie, Jurie J","Martin, R T W"]},{"key":"dc:creator","label":"Author","values":["De Jager, Pierre"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-09-14T12:14:24Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-09-14T12:14:24Z"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"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/11427/25167"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be considered a non-commutative composition operator) weighted by a partial isometry and/or a positive operator. In this thesis we describe the structures of isometries on various (non-commutative) symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing characterizations of extreme points in a certain class of Lorentz spaces and in various types of Orlicz spaces."]},{"key":"dc:title","label":"Title","values":["Isometries on symmetric spaces associated with semi-finite von Neumann algebras"]}]}],"canonical_facts":{"dc:contributor.advisor":["Conradie, Jurie J","Martin, R T W"],"dc:creator":["De Jager, Pierre"],"dc:date.accessioned":["2017-09-14T12:14:24Z"],"dc:date.available":["2017-09-14T12:14:24Z"],"dc:date.issued":["2017"],"dc:description.abstract":["Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be considered a non-commutative composition operator) weighted by a partial isometry and/or a positive operator. In this thesis we describe the structures of isometries on various (non-commutative) symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing characterizations of extreme points in a certain class of Lorentz spaces and in various types of Orlicz spaces."],"dc:identifier.uri":["http://hdl.handle.net/11427/25167"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Isometries on symmetric spaces associated with semi-finite von Neumann algebras"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:23:05Z"}