English

Spectra for Toeplitz Operators Associated with a Constrained Subalgebra

Functional Analysis 2022-10-12 v3 Complex Variables

Abstract

A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points a,bDa,b \in \mathbb{D}. This algebra serves as a multiplier algebra for the family of Hardy Hilbert spaces Ht2:={fH2:f(a)=tf(b)}H^2_t := \{ f\in H^2 : f(a)=tf(b)\}, where tC{}t\in \mathbb{C}\cup\{\infty\}. We show that various spectra of certain Toeplitz operators acting on these spaces are connected.

Keywords

Cite

@article{arxiv.2110.06379,
  title  = {Spectra for Toeplitz Operators Associated with a Constrained Subalgebra},
  author = {Christopher Felder and Douglas T. Pfeffer and Benjamin P. Russo},
  journal= {arXiv preprint arXiv:2110.06379},
  year   = {2022}
}

Comments

20 pages, no figures

R2 v1 2026-06-24T06:50:38.989Z