Abstract
dc:description.abstract<p>We will explore the numerical range of the block Toeplitz operator with symbol function \phi(z)=A0+zA1, where A0, A1 \in M2(\mathbb{C}). A full characterization of the numerical range of this operator proves to be quite difficult and so we will focus on characterizing the boundary of the related set, \{W(A0+zA1) : z \in \partial \mathbb{D}\}, in a specific case. We will use the theory of envelopes to explore what the boundary looks like and we will use geometric arguments to explore the number of flat portions on the boundary. We will then make a conjecture as to the number of flat portions on the boundary of the numerical range for any \(2 \times 2\) matrices A0 and A1. We finish by providing examples of flat portions on the boundary of the numerical range when A0, A1 \in Mn(\mathbb{C}), for \(3 \leq n \leq 5\).</p>
Degree
thesis:*- Name thesis:degree_name
- MS in Mathematics
- Discipline thesis:degree_discipline
- Mathematics
- Year dc:date.available
- 2022
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Randell, Brooke
- Contributors dc:contributor
-
- Linda Patton
- Mathematics
- College of Science and Mathematics
Subjects
dc:subject × 2Identifiers
dc:identifier.*- Identifier
- 10.15368/theses.2022.34
- OAI identifier oai:identifier
- oai:digitalcommons.calpoly.edu:theses-4042