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Spectra for Toeplitz Operators Associated with a Constrained Subalgebra

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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.

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Acknowledgements

The authors thank John McCarthy and Scott McCullough for helpful discussion, as well as the reviewer for their thoughtful suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, MO, 63130, USA

    Christopher Felder

  2. Department of Mathematics and Computer Science, Berry College, PO Box 495014, Mount Berry, GA, 30149-5014, USA

    Douglas T. Pfeffer

  3. Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    Benjamin P. Russo

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  1. Christopher Felder
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  2. Douglas T. Pfeffer
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  3. Benjamin P. Russo
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Correspondence to Christopher Felder.

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The first named author was supported in part by NSF Grant DMS-1565243. Notice: This manuscript has been authored, in part, by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

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Felder, C., Pfeffer, D.T. & Russo, B.P. Spectra for Toeplitz Operators Associated with a Constrained Subalgebra. Integr. Equ. Oper. Theory 94, 24 (2022). https://doi.org/10.1007/s00020-022-02700-9

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  • DOI: https://doi.org/10.1007/s00020-022-02700-9

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