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Subnormal operators, self-commutators, and pseudocontinuations

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Abstract

We study pure subnormal operators whose self-commutators have zero as an eigenvalue. We show that various questions in this are closely related to questions involving approximation by functions satisfying\(\bar \partial ^2 f = 0\) and to the study ofgeneralized quadrature domains.

First some general results are given that apply to all subnormal operators within this class; then we consider characterizing the analytic Toeplitz operators, the Hardy operators and cyclic subnormal operators whose self-commutators have zero as an eigenvalue.

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Authors and Affiliations

  1. Mathematics Department, Washington & Lee University, 24450, Lexington, VA

    Nathan S. Feldman

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  1. Nathan S. Feldman
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Feldman, N.S. Subnormal operators, self-commutators, and pseudocontinuations. Integr equ oper theory 37, 402–422 (2000). https://doi.org/10.1007/BF01192829

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  • DOI: https://doi.org/10.1007/BF01192829

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