Results for “constrained subalgebra”

Spectra for Toeplitz Operators Associated with a Constrained Subalgebra

A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points $a, b \in \mathbb{D}$. This algebra serves as a multiplier algebra for the family of Hardy Hilbert spaces $H^2_t := \{ f \in H^2 : tf(b)\}$ where $t \in \mathbb{C} \cup \{\infty\}$. We show that various spectra of certain Toeplitz operators acting on these spaces are connected.