Date of Award

2022

Document Type

Dissertation

Degree Name

Ph.D.

Organizational Unit

College of Natural Science and Mathematics, 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.

Rights Holder

Cheng-Chih Ko

Provenance

Received from ProQuest

File Format

application/pdf

Language

en

File Size

54 pgs

Discipline

Mathematics

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