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Dual Toeplitz Operators on the Sphere Via Spherical Isometries

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Abstract

We solve a characterization problem for dual Hardy-space Toeplitz operators on the unit sphere \({\mathbb{S}_{n}}\) in \({\mathbb{C}^{n}}\) posed by Guediri (Acta Math Sin (English series) 29(9):1791–1808, 2013). Our proof relies on the observation that dual Toeplitz operators on the orthogonal complement \({H^{2}(\mathbb{S}_{n})^{\bot}}\) of the Hardy space in L 2 can be viewed as Toeplitz operators with respect to a suitable spherical isometry. This correspondence also allows us to determine the commutator ideal of the dual Toeplitz C *-algebra.

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  1. Department of Mathematics, Saarland University, P.O. Box 15 11 50, 66041, Saarbrücken, Germany

    Michael Didas & Jörg Eschmeier

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  1. Michael Didas
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  2. Jörg Eschmeier
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Correspondence to Michael Didas.

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Didas, M., Eschmeier, J. Dual Toeplitz Operators on the Sphere Via Spherical Isometries. Integr. Equ. Oper. Theory 83, 291–300 (2015). https://doi.org/10.1007/s00020-015-2232-7

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  • DOI: https://doi.org/10.1007/s00020-015-2232-7

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