{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/34412"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/34412","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Gaussian-like von Neumann algebras and noncommutative brownian motion","abstract":"The $q$-Gaussian von Neumann algebras were first defined and studied by Bo\\.{z}ejko and Speicher in connection with noncommutative brownian motion. The main results of the present work is to establish that the $q$-Gaussian von Neumann algebras have the weak* completely contractive approximation property for all $-1 < q < 1$ and any number of generators, and they are strongly solid for all $-1 < q < 1$ and any finite number of generators.","abstract_html":"The $q$-Gaussian von Neumann algebras were first defined and studied by Bo\\.{z}ejko and Speicher in connection with noncommutative brownian motion. The main results of the present work is to establish that the $q$-Gaussian von Neumann algebras have the weak* completely contractive approximation property for all $-1 &lt; q &lt; 1$ and any number of generators, and they are strongly solid for all $-1 &lt; q &lt; 1$ and any finite number of generators.","abstract_has_math":true,"creators":["Avsec, Stephen"],"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","Baryshnikov, Yuliy","Athreya, Jayadev S."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-09-18T21:15:39Z","date_published":"2012-09-18T21:15:39Z","updated_at":"2026-07-22T22:25:31Z","subjects":["noncommutative probability","von Neumann algebras"],"languages":["en"],"rights":["Copyright 2012 Stephen Avsec"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/34412","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Junge, Marius","Boca, Florin","Baryshnikov, Yuliy","Athreya, Jayadev S."]},{"key":"dc:creator","label":"Author","values":["Avsec, Stephen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-09-18T21:15:39Z","2012-08"]},{"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":["noncommutative probability","von Neumann algebras"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 Stephen Avsec"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/34412"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The $q$-Gaussian von Neumann algebras were first defined and studied by Bo\\.{z}ejko and Speicher in connection with noncommutative brownian motion. The main results of the present work is to establish that the $q$-Gaussian von Neumann algebras have the weak* completely contractive approximation property for all $-1 < q < 1$ and any number of generators, and they are strongly solid for all $-1 < q < 1$ and any finite number of generators.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-10T14:41:29Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 avsec_stephen.pdf: 324913 bytes, checksum: de1a211dfbe2893e4b47d0943d2a834a (MD5)","Made available in DSpace on 2012-09-18T21:15:39Z (GMT). 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The main results of the present work is to establish that the $q$-Gaussian von Neumann algebras have the weak* completely contractive approximation property for all $-1 < q < 1$ and any number of generators, and they are strongly solid for all $-1 < q < 1$ and any finite number of generators.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-10T14:41:29Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 avsec_stephen.pdf: 324913 bytes, checksum: de1a211dfbe2893e4b47d0943d2a834a (MD5)","Made available in DSpace on 2012-09-18T21:15:39Z (GMT). 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