Spectra for Toeplitz Operators Associated with a Constrained Subalgebra
Abstract
A twopoint 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 $H^2_t := \{ f\in H^2 : f(a)=tf(b)\}$, where $t\in \mathbb{C}\cup\{\infty\}$. We show that various spectra of certain Toeplitz operators acting on these spaces are connected.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.06379
 Bibcode:
 2021arXiv211006379F
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Complex Variables;
 47A75 (Primary);
 47B35 (Secondary)
 EPrint:
 22 pages, no figures