A Banach space T1(d, θ) with a Tsirelson-type norm is constructed on the top of the topological Ramsey space T1 defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on each “branch” of the tree is shown to resemble the structure of an ℓ∞n+1 -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space T1(d, θ) is isomorphic to (∑n∊ℕ⊕ℓ∞n+1)p , where d ∈ ℕ with d ≥ 2, 0 < θ < 1, dθ > 1, and dθ = d1/p. Banach spaces with analogous norms are also constructed on extensions of the tree defined by Dobrinen and Todorcevic [6] and Trujillo [17]. They are shown to be isomorphic to (∑n∊ℕ⊕ℓ∞n+1)p as well.
","abstract_html":"<p>A Banach space <em>T<sub>1</sub>(d, θ)</em> with a Tsirelson-type norm is constructed on the top of the topological Ramsey space <em>T<sub>1</sub></em> defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on each “branch” of the tree is shown to resemble the structure of an ℓ<sub>∞</sub><sup>n+1</sup> -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space <em>T<sub>1</sub>(d, θ)</em> is isomorphic to (∑<sub>n∊ℕ</sub>⊕ℓ<sub>∞</sub><sup>n+1</sup>)<sub>p</sub> , where <em>d</em> ∈ ℕ with <em>d</em> ≥ 2, 0 < <em>θ</em> < 1, <em>dθ</em> > 1, and <em>dθ = d<sup>1/p</sup></em>. Banach spaces with analogous norms are also constructed on extensions of the tree defined by Dobrinen and Todorcevic [6] and Trujillo [17]. They are shown to be isomorphic to (∑<sub>n∊ℕ</sub>⊕ℓ<sub>∞</sub><sup>n+1</sup>)<sub>p </sub>as well.</p>","abstract_has_math":false,"creators":["Ko, Cheng-Chih"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Alvaro Arias","Kimon Valavanis","Frederic Latremoliere","Paul Horn"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-01-01T08:00:00Z","date_published":"2022-01-01T08:00:00Z","updated_at":"2026-07-24T02:02:53Z","subjects":["Analysis","Mathematics"],"languages":["en"],"rights":["Copyright is held by the author. User is responsible for all copyright compliance.
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.du.edu/etd/2135","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Alvaro Arias","Kimon Valavanis","Frederic Latremoliere","Paul Horn"]},{"key":"dc:creator","label":"Author","values":["Ko, Cheng-Chih"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Analysis","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the author. User is responsible for all copyright compliance.
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"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Banach Spaces on Topological Ramsey Structures"]}]}],"canonical_facts":{"dc:contributor":["Alvaro Arias","Kimon Valavanis","Frederic Latremoliere","Paul Horn"],"dc:creator":["Ko, Cheng-Chih"],"dc:description.abstract":["A Banach space T1(d, θ) with a Tsirelson-type norm is constructed on the top of the topological Ramsey space T1 defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on each “branch” of the tree is shown to resemble the structure of an ℓ∞n+1 -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space T1(d, θ) is isomorphic to (∑n∊ℕ⊕ℓ∞n+1)p , where d ∈ ℕ with d ≥ 2, 0 < θ < 1, dθ > 1, and dθ = d1/p. Banach spaces with analogous norms are also constructed on extensions of the tree defined by Dobrinen and Todorcevic [6] and Trujillo [17]. They are shown to be isomorphic to (∑n∊ℕ⊕ℓ∞n+1)p as well.
"],"dc:format":["application/pdf"],"dc:identifier":["https://digitalcommons.du.edu/etd/2135"],"dc:language":["en"],"dc:rights":["Copyright is held by the author. User is responsible for all copyright compliance.
"],"dc:subject":["Analysis","Mathematics"],"dc:title":["Banach Spaces on Topological Ramsey Structures"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T02:02:53Z"}