Date of Award
2022
Document Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
Alvaro Arias
Second Advisor
Kimon Valavanis
Third Advisor
Frederic Latremoliere
Fourth Advisor
Paul Horn
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.
Publication Statement
Copyright is held by the author. User is responsible for all copyright compliance.
Recommended Citation
Ko, Cheng-Chih, "Banach Spaces on Topological Ramsey Structures" (2022). Electronic Theses and Dissertations. 2135.
https://digitalcommons.du.edu/etd/2135
Provenance
Received from ProQuest
Rights holder
Cheng-Chih Ko
File size
54 pgs
Copyright date
2022
File format
application/pdf
Language
en
Discipline
Mathematics