Banach Spaces on Topological Ramsey Structures

<p>A Banach space <em>T₁(d, θ)</em> with a Tsirelson-type norm is constructed on the top of the topological Ramsey space <em>T₁</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_∞ⁿ⁺¹ -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space <em>T₁(d, θ)</em> is isomorphic to (∑_n∊ℕ⊕ℓ_∞ⁿ⁺¹)_p , where <em>d</em> ∈ ℕ with <em>d</em> ≥ 2, 0 < <em>θ</em> < 1, <em>dθ</em> > 1, and <em>dθ = d^1/p</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 (∑_n∊ℕ⊕ℓ_∞ⁿ⁺¹)_pas well.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Year

2022

Author dc:creator

• Ko, Cheng-Chih

Contributors dc:contributor

• Alvaro Arias
• Kimon Valavanis
• Frederic Latremoliere
• Paul Horn

• Analysis
• Mathematics

Statement dc:rights

• <p>Copyright is held by the author. User is responsible for all copyright compliance.</p>

Language dc:language

en

Repository record dc:identifier

https://digitalcommons.du.edu/etd/2135

OAI identifier oai:identifier

oai:digitalcommons.du.edu:etd-3121