{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/97307"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/97307","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Approximating rotation algebras and inclusions of C*-algebras","abstract":"In the first part of this thesis, we will follow Kirchberg’s categorical perspective to establish new notions of WEP and QWEP relative to a C∗-algebra, and develop similar properties as in the classical WEP and QWEP. Also we will show some examples of relative WEP and QWEP to illustrate the relations with the classical cases. The focus of the second part of this thesis is the approximation of rotation algebras in the quantum Gromov–Hausdorff distance. We introduce the completely bounded quantum Gromov–Hausdorff distance and show that for even dimensions, the higher dimensional rotation algebras can be approximated by matrix algebras in this sense. Finally, we show that for even dimensions, matrix algebras converge to the rotation algebras in the strongest form of Gromov–Hausdorff distance, namely in the sense of Latrémolière’s Gromov–Hausdorff propinquity.","abstract_html":"In the first part of this thesis, we will follow Kirchberg’s categorical perspective to establish new notions of WEP and QWEP relative to a C∗-algebra, and develop similar properties as in the classical WEP and QWEP. Also we will show some examples of relative WEP and QWEP to illustrate the relations with the classical cases. The focus of the second part of this thesis is the approximation of rotation algebras in the quantum Gromov–Hausdorff distance. We introduce the completely bounded quantum Gromov–Hausdorff distance and show that for even dimensions, the higher dimensional rotation algebras can be approximated by matrix algebras in this sense. Finally, we show that for even dimensions, matrix algebras converge to the rotation algebras in the strongest form of Gromov–Hausdorff distance, namely in the sense of Latrémolière’s Gromov–Hausdorff propinquity.","abstract_has_math":false,"creators":["Rezvani, Sepideh"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Junge, Marius","Boca, Florin","Ruan, Zhong-Jin","Oikhberg, Timur"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-10T19:14:44Z","date_published":"2017-08-10T19:14:44Z","updated_at":"2026-07-22T22:24:32Z","subjects":["C*-algebras","Weak expectation property (WEP)","Quotient weak expectation property (QWEP)","A-WEP","A-QWEP","Relatively weak injectivity","Order-unit space","Noncommutative tori","Compact quantum metric space","Conditionally negative length function","Heat semigroup","Poisson semigroup","Rotation algebra","Continuous field of compact quantum metric spaces","Gromov–Hausdorff distance","Completely bounded quantum Gromov–Hausdorff distance","Gromov–Hausdorff propinquity"],"languages":["en"],"rights":["Copyright 2017 Sepideh Rezvani"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/97307","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Junge, Marius","Boca, Florin","Ruan, Zhong-Jin","Oikhberg, Timur"]},{"key":"dc:creator","label":"Author","values":["Rezvani, Sepideh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-08-10T19:14:44Z","2017-04-06","2017-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["C*-algebras","Weak expectation property (WEP)","Quotient weak expectation property (QWEP)","A-WEP","A-QWEP","Relatively weak injectivity","Order-unit space","Noncommutative tori","Compact quantum metric space","Conditionally negative length function","Heat semigroup","Poisson semigroup","Rotation algebra","Continuous field of compact quantum metric spaces","Gromov–Hausdorff distance","Completely bounded quantum Gromov–Hausdorff distance","Gromov–Hausdorff propinquity"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Sepideh Rezvani"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/97307"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In the first part of this thesis, we will follow Kirchberg’s categorical perspective to establish new notions of WEP and QWEP relative to a C∗-algebra, and develop similar properties as in the classical WEP and QWEP. Also we will show some examples of relative WEP and QWEP to illustrate the relations with the classical cases. The focus of the second part of this thesis is the approximation of rotation algebras in the quantum Gromov–Hausdorff distance. We introduce the completely bounded quantum Gromov–Hausdorff distance and show that for even dimensions, the higher dimensional rotation algebras can be approximated by matrix algebras in this sense. Finally, we show that for even dimensions, matrix algebras converge to the rotation algebras in the strongest form of Gromov–Hausdorff distance, namely in the sense of Latrémolière’s Gromov–Hausdorff propinquity.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Sepideh Rezvani, accepted the attached license on 2017-04-05 at 17:43.","The student, Sepideh Rezvani, submitted this Dissertation for approval on 2017-04-05 at 18:02.","This Dissertation was approved for publication on 2017-04-06 at 13:59.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10656 on 2017-08-10 at 13:38:49","Made available in DSpace on 2017-08-10T19:14:44Z (GMT). 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Also we will show some examples of relative WEP and QWEP to illustrate the relations with the classical cases. The focus of the second part of this thesis is the approximation of rotation algebras in the quantum Gromov–Hausdorff distance. We introduce the completely bounded quantum Gromov–Hausdorff distance and show that for even dimensions, the higher dimensional rotation algebras can be approximated by matrix algebras in this sense. Finally, we show that for even dimensions, matrix algebras converge to the rotation algebras in the strongest form of Gromov–Hausdorff distance, namely in the sense of Latrémolière’s Gromov–Hausdorff propinquity.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Sepideh Rezvani, accepted the attached license on 2017-04-05 at 17:43.","The student, Sepideh Rezvani, submitted this Dissertation for approval on 2017-04-05 at 18:02.","This Dissertation was approved for publication on 2017-04-06 at 13:59.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10656 on 2017-08-10 at 13:38:49","Made available in DSpace on 2017-08-10T19:14:44Z (GMT). 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