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A Note on the Range of Toeplitz Operators

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Abstract.

A well known lemma attributed to Coburn states that a Toeplitz operator with non-trivial kernel acting on the Hardy space must have dense range. We show that the range of a non-zero Toeplitz operator with non-trivial kernel must contain all polynomials and state this in a precise form.

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  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Dragan Vukotić

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  1. Dragan Vukotić
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Correspondence to Dragan Vukotić.

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Vukotić, D. A Note on the Range of Toeplitz Operators. Integr. equ. oper. theory 50, 565–567 (2004). https://doi.org/10.1007/s00020-004-1312-x

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  • DOI: https://doi.org/10.1007/s00020-004-1312-x

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