Speaker
Linda Patton
(Cal Poly San Luis Obispo)
Description
Using results from Brown-Halmos, Klein (1972) described the numerical range of a general Toeplitz operator on $H^2(\mathbb{D})$. In particular, the numerical range of a Toeplitz operator $T_p$ with polynomial symbol $p$ is the convex hull of the image of the unit disk under $p$. By analyzing $p(\mathbb{T})$ and its relationship to the Kippenhahn curve of a matrix, we provide conditions under which the closure of $W(T_p)$ is the numerical range of a finite matrix $M_p$. Results about the eigenvalues of $M_p$ will be discussed as well.
Author
Linda Patton
(Cal Poly San Luis Obispo)