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 ℓn+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⊕ℓn+1)p , where d ∈ ℕ with d ≥ 2, 0 < θ < 1, > 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⊕ℓn+1)p as well.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Provenance

Received from ProQuest

Rights holder

Cheng-Chih Ko

File size

54 pgs

File format

application/pdf

Language

en

Discipline

Mathematics



Included in

Analysis Commons

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