Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Other Mathematics
Exploring The Numerical Range Of Block Toeplitz Operators, Brooke Randell
Exploring The Numerical Range Of Block Toeplitz Operators, Brooke Randell
Master's Theses
We will explore the numerical range of the block Toeplitz operator with symbol function \(\phi(z)=A_0+zA_1\), where \(A_0, A_1 \in M_2(\mathbb{C})\). 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, \(\{W(A_0+zA_1) : z \in \partial \mathbb{D}\}\), 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 …
Van Kampen Diagrams And Small Cancellation Theory, Kelsey N. Lowrey
Van Kampen Diagrams And Small Cancellation Theory, Kelsey N. Lowrey
Master's Theses
On The Numerical Range Of Compact Operators, Montserrat Dabkowski
On The Numerical Range Of Compact Operators, Montserrat Dabkowski
Master's Theses
One of the many characterizations of compact operators is as linear operators which
can be closely approximated by bounded finite rank operators (theorem 25). It is
well known that the numerical range of a bounded operator on a finite dimensional
Hilbert space is closed (theorem 54). In this thesis we explore how close to being
closed the numerical range of a compact operator is (theorem 56). We also describe
how limited the difference between the closure and the numerical range of a compact
operator can be (theorem 58). To aid in our exploration of the numerical range of
a compact …