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 $H^2_t := \{ f\in H^2 : f(a)=tf(b)\}$, where $t\in \mathbb{C}\cup\{\infty\}$. We show that various spectra of certain Toeplitz operators acting on these spaces are connected.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2021
- arXiv:
- arXiv:2110.06379
- Bibcode:
- 2021arXiv211006379F
- Keywords:
-
- Mathematics - Functional Analysis;
- Mathematics - Complex Variables;
- 47A75 (Primary);
- 47B35 (Secondary)
- E-Print:
- 22 pages, no figures