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Szegő and Widom Theorems for Finite Codimensional Subalgebras of a Class of Uniform Algebras

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Abstract

We establish versions of Szegő’s distance formula and Widom’s theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear constraints. Each such algebra is naturally represented on a family of reproducing kernel Hilbert spaces, which play a central role in the proofs.

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Authors and Affiliations

  1. Department of Mathematics, Berry College, PO Box 495014, Mount Berry, GA, 30149-5014, USA

    Douglas T. Pfeffer

  2. Department of Mathematics, University of Florida, PO Box 118105, Gainesville, FL, 32611-8105, USA

    Michael T. Jury

Authors
  1. Douglas T. Pfeffer
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  2. Michael T. Jury
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Correspondence to Douglas T. Pfeffer.

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Communicated by Ding-Xuan Zhou.

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Portions of this work appeared in the first named author’s PhD dissertation, given at the University of Florida, May 2019

Second named author partially supported by NSF Grant DMS-1900364.

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Pfeffer, D.T., Jury, M.T. Szegő and Widom Theorems for Finite Codimensional Subalgebras of a Class of Uniform Algebras. Complex Anal. Oper. Theory 15, 83 (2021). https://doi.org/10.1007/s11785-021-01129-z

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