University of Illinois Urbana-Champaign

Topics on the geometry and classification of Banach lattices

Gramcko-Tursi, Mary Angelica

Content Files
GRAMCKO-TURSI-DISSERTATION-2021.pdf

Permalink

https://hdl.handle.net/2142/110490

Description

Title
Topics on the geometry and classification of Banach lattices
Author(s)
Gramcko-Tursi, Mary Angelica
Issue Date
2021-04-19
Director of Research (if dissertation) or Advisor (if thesis)
Oikhberg, Timur
Doctoral Committee Chair(s)
Junge, Marius
Committee Member(s)
  • Kutzarova, Denka
  • Tserunyan, Anush
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2021-09-17T01:11:00Z
Keyword(s)
  • Banach lattices
  • universal spaces
  • standard Borel spaces
  • Isomorphism equivalence relations
  • Fraisse limits
  • homogeneity
  • renormings
Abstract
We examine topics related to the geometric structure of Banach lattices of various classes, their properties, and classification using tools from functional analysis and mathematical logic. This work can be roughly divided into four parts. The first part (Chapter 2) presents several geometric results on Banach lattice analogues of classical Banach space theorems which ground results from later sections. The second part (Chapters 3 and 4) presents various results on the descriptive complexity of classes of Banach lattices and determines the complexity of the lattice isomorphism and isometry equivalence relations. The focus of the third part (Chapter 5) is the construction of a lattice isometrically universal separable ”Gurarij” Banach lattice by combining properties of the geometric structure of Banach lattices with Fraısse machinery that was developed in the context of continuous logic. Finally, we return to geometric considerations in the fourth and last part of chapter 6, which describes a method of renorming AM spaces so that the only lattice isometry is the trivial isometry.
Graduation Semester
2021-05
Type of Resource
Thesis
Permalink
http://hdl.handle.net/2142/110490
Copyright and License Information
Copyright 2021 Mary Gramcko-Tursi

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Mathematics