{"id":{"repo_id":"vcu","oai_identifier":"oai:scholarscompass.vcu.edu:etd-1552"},"canonical_url":"https://search.dev.ndltd.org/etd/vcu/oai:scholarscompass.vcu.edu:etd-1552","repository":{"repo_id":"vcu","name":"Virginia Commonwealth University","base_url":"https://scholarscompass.vcu.edu/do/oai/"},"display":{"title":"Properties and Legacies of Tsirelson Space","abstract":"Tsirelson space is a reflexive, separable Banach space constructed by Boris Tsirelson to be the first example of a Banach space that does not contain an isomorphic copy of the sequence spaces c_0 or l_p for 1\\leqslant p<infinity. We begin with the construction of the classical sequence spaces c_0 and l_p for 1\\leqslant p<infinity by taking the completion of c_00 with respect to their norms. The proofs of non-embedding of various sequence spaces into Schreier space and Baernstein space then prepare us for the main result: the proof of the non-embedding of c_0 and l_p from 1\\leqslant p< infinity in Tsirelson space. We close by discussing further properties of Tsirelson space, including reflexivity and distortability.","abstract_html":"Tsirelson space is a reflexive, separable Banach space constructed by Boris Tsirelson to be the first example of a Banach space that does not contain an isomorphic copy of the sequence spaces c_0 or l_p for 1\\leqslant p&lt;infinity. We begin with the construction of the classical sequence spaces c_0 and l_p for 1\\leqslant p&lt;infinity by taking the completion of c_00 with respect to their norms. The proofs of non-embedding of various sequence spaces into Schreier space and Baernstein space then prepare us for the main result: the proof of the non-embedding of c_0 and l_p from 1\\leqslant p&lt; infinity in Tsirelson space. We close by discussing further properties of Tsirelson space, including reflexivity and distortability.","abstract_has_math":false,"creators":["Hoeft, Alexandra"],"institution":null,"degree_name":"Master of Science","degree_level":"Thesis","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Kevin Beanland"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-05-01T07:00:00Z","date_published":"2013-05-01T07:00:00Z","updated_at":"2026-07-24T05:54:02Z","subjects":["Functional Analysis","Physical Sciences and Mathematics"],"languages":[],"rights":["© The Author"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarscompass.vcu.edu/etd/553"],"render_values":[{"text":"https://scholarscompass.vcu.edu/etd/553","href":"https://scholarscompass.vcu.edu/etd/553","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.25772/J32S-HP41","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kevin Beanland"]},{"key":"dc:creator","label":"Author","values":["Hoeft, Alexandra"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2213-10-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Functional Analysis","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© The Author"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.25772/J32S-HP41","https://scholarscompass.vcu.edu/etd/553"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Tsirelson space is a reflexive, separable Banach space constructed by Boris Tsirelson to be the first example of a Banach space that does not contain an isomorphic copy of the sequence spaces c_0 or l_p for 1\\leqslant p<infinity. We begin with the construction of the classical sequence spaces c_0 and l_p for 1\\leqslant p<infinity by taking the completion of c_00 with respect to their norms. The proofs of non-embedding of various sequence spaces into Schreier space and Baernstein space then prepare us for the main result: the proof of the non-embedding of c_0 and l_p from 1\\leqslant p< infinity in Tsirelson space. We close by discussing further properties of Tsirelson space, including reflexivity and distortability."]},{"key":"dc:title","label":"Title","values":["Properties and Legacies of Tsirelson Space"]}]}],"canonical_facts":{"dc:contributor":["Kevin Beanland"],"dc:creator":["Hoeft, Alexandra"],"dc:date.available":["2213-10-17T07:00:00Z"],"dc:description.abstract":["Tsirelson space is a reflexive, separable Banach space constructed by Boris Tsirelson to be the first example of a Banach space that does not contain an isomorphic copy of the sequence spaces c_0 or l_p for 1\\leqslant p<infinity. We begin with the construction of the classical sequence spaces c_0 and l_p for 1\\leqslant p<infinity by taking the completion of c_00 with respect to their norms. The proofs of non-embedding of various sequence spaces into Schreier space and Baernstein space then prepare us for the main result: the proof of the non-embedding of c_0 and l_p from 1\\leqslant p< infinity in Tsirelson space. We close by discussing further properties of Tsirelson space, including reflexivity and distortability."],"dc:identifier":["https://doi.org/10.25772/J32S-HP41","https://scholarscompass.vcu.edu/etd/553"],"dc:rights":["© The Author"],"dc:subject":["Functional Analysis","Physical Sciences and Mathematics"],"dc:title":["Properties and Legacies of Tsirelson Space"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T05:54:02Z"}