Spectra for Toeplitz Operators Associated with a Constrained Subalgebra

Abstract

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 $H_t^2:=\{f\in H^2:f(a)=tf(b)\}$, where $t\in \mathbb{C}\cup \{\infty \}$. We show that various spectra of certain Toeplitz operators acting on these spaces are connected.

20 pages, no figures