{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/9184"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/9184","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Properties of Pure Completely Positive Linear Maps of Operator Systems","abstract":"If 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.","abstract_html":"If 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.","abstract_has_math":false,"creators":["Tessier, Ryan Brett"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral -- first","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Farenick, Douglas"],"committee_chairs":[],"committee_members":["Floricel, Remus","Plosker, Sarah","Zilles, Sandra"],"year":2020,"date_issued":"2020-02","date_published":"2020-02","updated_at":"2026-07-24T04:03:38Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4445"],"render_values":[{"text":"https://doi.org/10.82465/4445","href":"https://doi.org/10.82465/4445","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/9184","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Farenick, Douglas"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Floricel, Remus","Plosker, Sarah","Zilles, Sandra"]},{"key":"dc:creator","label":"Author","values":["Tessier, Ryan Brett"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-08-26T22:31:36Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-08-26T22:31:36Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-02"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral -- first"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4445"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/9184"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A 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."]},{"key":"dc:description.abstract","label":"Abstract","values":["If 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."]},{"key":"dc:title","label":"Title","values":["Properties of Pure Completely Positive Linear Maps of Operator Systems"]}]}],"canonical_facts":{"dc:contributor.advisor":["Farenick, Douglas"],"dc:contributor.committeemember":["Floricel, Remus","Plosker, Sarah","Zilles, Sandra"],"dc:creator":["Tessier, Ryan Brett"],"dc:date.accessioned":["2020-08-26T22:31:36Z"],"dc:date.available":["2020-08-26T22:31:36Z"],"dc:date.issued":["2020-02"],"dc:description":["A 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."],"dc:description.abstract":["If 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."],"dc:identifier.doi":["https://doi.org/10.82465/4445"],"dc:identifier.uri":["https://hdl.handle.net/10294/9184"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Properties of Pure Completely Positive Linear Maps of Operator Systems"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral -- first"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:38Z"}