{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/3561"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/3561","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"The Structure of Operator Systems on Finite-Dimensional Hilbert Spaces","abstract":"The purpose of this thesis is to describe in detail the structure of arbitrary operator systems S B(H), where H is assumed to be of finite dimension, using Arveson's non-commutative Choquet theory, and to determine the C* -envelope of S in certain special cases of interest. Arveson classifies these operator systems as either reduced or non-reduced, and we look at these classifications in detail. S is said to be reduced when its boundary ideal is {0} and non-reduced otherwise. We will give examples of 2-dimensional and 3-dimensional operator systems; show what Arveson's parametrization would be in such cases; and determine the C*-envelopes and boundary ideals.","abstract_html":"The purpose of this thesis is to describe in detail the structure of arbitrary operator systems S B(H), where H is assumed to be of finite dimension, using Arveson's non-commutative Choquet theory, and to determine the C* -envelope of S in certain special cases of interest. Arveson classifies these operator systems as either reduced or non-reduced, and we look at these classifications in detail. S is said to be reduced when its boundary ideal is {0} and non-reduced otherwise. We will give examples of 2-dimensional and 3-dimensional operator systems; show what Arveson's parametrization would be in such cases; and determine the C*-envelopes and boundary ideals.","abstract_has_math":false,"creators":["Mwangangi, Sadia Hassan"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Science (MSc)","degree_level":"Master's","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Argerami, Martin"],"committee_chairs":[],"committee_members":["Farenick, Douglas","Floricel, Remus"],"year":2012,"date_issued":"2012-04","date_published":"2012-04","updated_at":"2026-07-24T04:03:45Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4794"],"render_values":[{"text":"https://doi.org/10.82465/4794","href":"https://doi.org/10.82465/4794","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/3561","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Argerami, Martin"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Farenick, Douglas","Floricel, Remus"]},{"key":"dc:creator","label":"Author","values":["Mwangangi, Sadia Hassan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2012-08-31T16:38:02Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2012-08-31T16:38:02Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-04"]},{"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":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"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/10.82465/4794"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/3561"]}]},{"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 Master of Science degree in Mathematics, University of Regina. v, 65 l."]},{"key":"dc:description.abstract","label":"Abstract","values":["The purpose of this thesis is to describe in detail the structure of arbitrary operator systems S B(H), where H is assumed to be of finite dimension, using Arveson's non-commutative Choquet theory, and to determine the C* -envelope of S in certain special cases of interest. Arveson classifies these operator systems as either reduced or non-reduced, and we look at these classifications in detail. S is said to be reduced when its boundary ideal is {0} and non-reduced otherwise. We will give examples of 2-dimensional and 3-dimensional operator systems; show what Arveson's parametrization would be in such cases; and determine the C*-envelopes and boundary ideals."]},{"key":"dc:title","label":"Title","values":["The Structure of Operator Systems on Finite-Dimensional Hilbert Spaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Argerami, Martin"],"dc:contributor.committeemember":["Farenick, Douglas","Floricel, Remus"],"dc:creator":["Mwangangi, Sadia Hassan"],"dc:date.accessioned":["2012-08-31T16:38:02Z"],"dc:date.available":["2012-08-31T16:38:02Z"],"dc:date.issued":["2012-04"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science degree in Mathematics, University of Regina. v, 65 l."],"dc:description.abstract":["The purpose of this thesis is to describe in detail the structure of arbitrary operator systems S B(H), where H is assumed to be of finite dimension, using Arveson's non-commutative Choquet theory, and to determine the C* -envelope of S in certain special cases of interest. Arveson classifies these operator systems as either reduced or non-reduced, and we look at these classifications in detail. S is said to be reduced when its boundary ideal is {0} and non-reduced otherwise. We will give examples of 2-dimensional and 3-dimensional operator systems; show what Arveson's parametrization would be in such cases; and determine the C*-envelopes and boundary ideals."],"dc:identifier.doi":["https://doi.org/10.82465/4794"],"dc:identifier.uri":["https://hdl.handle.net/10294/3561"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["The Structure of Operator Systems on Finite-Dimensional Hilbert Spaces"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:45Z"}