Isometries on symmetric spaces associated with semi-finite von Neumann algebras

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dc.contributor.advisorConradie, Jurie Jen_ZA
dc.contributor.advisorMartin, R T Wen_ZA
dc.contributor.authorDe Jager, Pierreen_ZA
dc.date.accessioned2017-09-14T12:14:24Z
dc.date.available2017-09-14T12:14:24Z
dc.date.issued2017en_ZA
dc.description.abstractIsometries 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.en_ZA
dc.identifier.apacitationDe Jager, P. (2017). <i>Isometries on symmetric spaces associated with semi-finite von Neumann algebras</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/25167en_ZA
dc.identifier.chicagocitationDe Jager, Pierre. <i>"Isometries on symmetric spaces associated with semi-finite von Neumann algebras."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017. http://hdl.handle.net/11427/25167en_ZA
dc.identifier.citationDe Jager, P. 2017. Isometries on symmetric spaces associated with semi-finite von Neumann algebras. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - De Jager, Pierre AB - 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. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Isometries on symmetric spaces associated with semi-finite von Neumann algebras TI - Isometries on symmetric spaces associated with semi-finite von Neumann algebras UR - http://hdl.handle.net/11427/25167 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/25167
dc.identifier.vancouvercitationDe Jager P. Isometries on symmetric spaces associated with semi-finite von Neumann algebras. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/25167en_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.otherMathematicsen_ZA
dc.titleIsometries on symmetric spaces associated with semi-finite von Neumann algebrasen_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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