Subproduct and Product Systems of C* - Algebras

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dc.contributor.advisorFloricel, Remus
dc.contributor.authorKetelboeter, Brian
dc.contributor.committeememberFarenick, Douglas
dc.contributor.committeememberArgerami, Martin
dc.contributor.committeememberMobed, Nader
dc.contributor.externalexaminerWang, Jiun-Chau
dc.date.accessioned2020-08-26T22:20:58Z
dc.date.available2020-08-26T22:20:58Z
dc.date.issued2019-08
dc.descriptionA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics, University of Regina. iv, 70 p.en_US
dc.description.abstractThis thesis initiates the theory of Tsirelson C -subproduct and product systems on a solid basis of results, which extends Arveson's theory of product systems of Hilbert spaces, with emphasis on Tsirelson's two parameter version of product systems of Hilbert spaces. Within we prove that every Tsirelson C -subproduct system admits a Bhat-type dilation to a Tsirelson C -product system, analogous to the Bhat dilation of a conservative quantum dynamical semigorup to an E0-semigroup. We also construct the universal C -algebra of an arbitrary unital Tsirelson C -subproduct system that, together with its associated quantum L evy process, reflect the behavior of the system. Finally, we provide a Arveson-Powers classi cation type scheme of unital Tsirelson C -subproduct and product systems, based on the concept of unit. We also give a description of the units of a spatial Tsirelson C -subproduct system at the level of the state-space of its universal C -algebra, and show that every unit gives rise to an algebraic Tsirelson subproduct system of Hilbert spaces via the GNS construction.en_US
dc.description.authorstatusStudenten
dc.description.peerreviewyesen
dc.identifier.tcnumberTC-SRU-9171
dc.identifier.thesisurlhttps://ourspace.uregina.ca/bitstream/handle/10294/9171/Ketelboeter_Brian_PhD_Math_Spring2020.pdf
dc.identifier.urihttps://hdl.handle.net/10294/9171
dc.language.isoenen_US
dc.publisherFaculty of Graduate Studies and Research, University of Reginaen_US
dc.titleSubproduct and Product Systems of C* - Algebrasen_US
dc.typeThesisen
thesis.degree.departmentDepartment of Mathematics and Statisticsen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Reginaen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophy (PhD)en_US
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