Jordan homomorphisms and derivations on algebras of measurable operators

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dc.contributor.advisorConradie, JJen_ZA
dc.contributor.authorWeigt, Martinen_ZA
dc.date.accessioned2014-07-31T08:11:11Z
dc.date.available2014-07-31T08:11:11Z
dc.date.issued2008en_ZA
dc.descriptionIncludes abstract.
dc.descriptionIncludes bibliographical references (p.122-132) and index.
dc.description.abstractA 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.en_ZA
dc.identifier.apacitationWeigt, M. (2008). <i>Jordan homomorphisms and derivations on 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/11427/4944en_ZA
dc.identifier.chicagocitationWeigt, Martin. <i>"Jordan homomorphisms and derivations on algebras of measurable operators."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2008. http://hdl.handle.net/11427/4944en_ZA
dc.identifier.citationWeigt, M. 2008. Jordan homomorphisms and derivations on algebras of measurable operators. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Weigt, Martin AB - 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. DA - 2008 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2008 T1 - Jordan homomorphisms and derivations on algebras of measurable operators TI - Jordan homomorphisms and derivations on algebras of measurable operators UR - http://hdl.handle.net/11427/4944 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/4944
dc.identifier.vancouvercitationWeigt M. Jordan homomorphisms and derivations on 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/11427/4944en_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.titleJordan homomorphisms and derivations on 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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