{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/4944"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/4944","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Jordan homomorphisms and derivations on algebras of measurable operators","abstract":"A few decades ago, Kaplansky raised the question whether unital linear invertibility preserving maps between unital algebras are Jordan homomorphisms. This question is still unanswered, and the progress that has been made has mainly been in the context of Banach algebras, including C*-algebras and von Neumann algebras. Let M be a von Neumann algebra with a faithful semifinite normal trace τ , and M~ the algebra of τ-measurable operators (measurable for short) affiliated with M. The algebra M~ can be endowed with a topology Уcm, called the topology of convergence in measure, such that M~ becomes a complete metrizable topological *-algebra in which M is dense. One of the aims of this thesis is to find answers to Kaplansky’s question in the context of algebras of measurable operators.","abstract_html":"A few decades ago, Kaplansky raised the question whether unital linear invertibility preserving maps between unital algebras are Jordan homomorphisms. This question is still unanswered, and the progress that has been made has mainly been in the context of Banach algebras, including C*-algebras and von Neumann algebras. Let M be a von Neumann algebra with a faithful semifinite normal trace τ , and M~ the algebra of τ-measurable operators (measurable for short) affiliated with M. The algebra M~ can be endowed with a topology Уcm, called the topology of convergence in measure, such that M~ becomes a complete metrizable topological *-algebra in which M is dense. One of the aims of this thesis is to find answers to Kaplansky’s question in the context of algebras of measurable operators.","abstract_has_math":false,"creators":["Weigt, Martin"],"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":"2026-07-22T22:23:24Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/4944","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":["Weigt, Martin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-07-31T08:11:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-07-31T08:11:11Z"]},{"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/11427/4944"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes abstract.","Includes bibliographical references (p.122-132) and index."]},{"key":"dc:description.abstract","label":"Abstract","values":["A few decades ago, Kaplansky raised the question whether unital linear invertibility preserving maps between unital algebras are Jordan homomorphisms. This question is still unanswered, and the progress that has been made has mainly been in the context of Banach algebras, including C*-algebras and von Neumann algebras. Let M be a von Neumann algebra with a faithful semifinite normal trace τ , and M~ the algebra of τ-measurable operators (measurable for short) affiliated with M. The algebra M~ can be endowed with a topology Уcm, called the topology of convergence in measure, such that M~ becomes a complete metrizable topological *-algebra in which M is dense. One of the aims of this thesis is to find answers to Kaplansky’s question in the context of algebras of measurable operators."]},{"key":"dc:title","label":"Title","values":["Jordan homomorphisms and derivations on algebras of measurable operators"]}]}],"canonical_facts":{"dc:contributor.advisor":["Conradie, JJ"],"dc:creator":["Weigt, Martin"],"dc:date.accessioned":["2014-07-31T08:11:11Z"],"dc:date.available":["2014-07-31T08:11:11Z"],"dc:date.issued":["2008"],"dc:description":["Includes abstract.","Includes bibliographical references (p.122-132) and index."],"dc:description.abstract":["A few decades ago, Kaplansky raised the question whether unital linear invertibility preserving maps between unital algebras are Jordan homomorphisms. This question is still unanswered, and the progress that has been made has mainly been in the context of Banach algebras, including C*-algebras and von Neumann algebras. Let M be a von Neumann algebra with a faithful semifinite normal trace τ , and M~ the algebra of τ-measurable operators (measurable for short) affiliated with M. The algebra M~ can be endowed with a topology Уcm, called the topology of convergence in measure, such that M~ becomes a complete metrizable topological *-algebra in which M is dense. One of the aims of this thesis is to find answers to Kaplansky’s question in the context of algebras of measurable operators."],"dc:identifier.uri":["http://hdl.handle.net/11427/4944"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Jordan homomorphisms and derivations on algebras of measurable operators"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:23:24Z"}