Date of Award
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 . 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  and Trujillo . They are shown to be isomorphic to (∑n∊ℕ⊕ℓ∞n+1)p as well.
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Ko, Cheng-Chih, "Banach Spaces on Topological Ramsey Structures" (2022). Electronic Theses and Dissertations. 2135.
Received from ProQuest