Properties of Pure Completely Positive Linear Maps of Operator Systems

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dc.contributor.advisorFarenick, Douglas
dc.contributor.authorTessier, Ryan Brett
dc.contributor.committeememberFloricel, Remus
dc.contributor.committeememberPlosker, Sarah
dc.contributor.committeememberZilles, Sandra
dc.contributor.externalexaminerClouatre, Raphael
dc.date.accessioned2020-08-26T22:31:36Z
dc.date.available2020-08-26T22:31:36Z
dc.date.issued2020-02
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. ix, 74 p.en_US
dc.description.abstractIf Sn denotes the (2n + 1)-dimensional operator system spanned in the group C*-algebra C*(Fn) by the n generators of the free group Fn and their inverses, then the identity map in : Sn -> Sn is shown to be a pure completely positive map. Similarly, the identity map jn : NC(n) -> NC(n) on the noncommutative n-cube NC(n) in the group C_-algebra of the free product of n copies of Z2 is also shown to be pure. Further results on the purity of the reductions of the tensor product of pure completely positive maps are given. Some previously unrecorded generic features of pure completely positive linear maps are also presented, including a result on the pure extendibility of pure completely positive linear maps on operator systems with values in an injective von Neumann algebra.en_US
dc.description.authorstatusStudenten
dc.description.peerreviewyesen
dc.identifier.tcnumberTC-SRU-9184
dc.identifier.thesisurlhttps://ourspace.uregina.ca/bitstream/handle/10294/9184/Tessier_Ryan_PhD_MATH_Spring2020.pdf
dc.identifier.urihttps://hdl.handle.net/10294/9184
dc.language.isoenen_US
dc.publisherFaculty of Graduate Studies and Research, University of Reginaen_US
dc.titleProperties of Pure Completely Positive Linear Maps of Operator Systemsen_US
dc.typeThesisen_US
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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