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On a theorem of Bishop and commutants of Toeplitz operators in \(\mathbb {C}^n\)

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Abstract

We prove an approximation theorem on a class of domains in \(\mathbb {C}^n\) on which the \(\overline{\partial }\)-problem is solvable in \(L^{\infty }\). Furthermore, as a corollary, we obtain a version of the Axler–Čučković–Rao theorem in higher dimensions.

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Acknowledgements

We would like to thank Alexander Izzo for reading an earlier manuscript of this paper and for providing us with valuable comments. We are also thankful to the anonymous referee for helpful feedback.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Toledo, Toledo, OH, 43606, USA

    Sönmez Şahutoğlu & Akaki Tikaradze

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  1. Sönmez Şahutoğlu
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  2. Akaki Tikaradze
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Correspondence to Sönmez Şahutoğlu.

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The second author is supported in part by the University of Toledo Summer Research Awards and Fellowships Program.

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Şahutoğlu, S., Tikaradze, A. On a theorem of Bishop and commutants of Toeplitz operators in \(\mathbb {C}^n\). Rend. Circ. Mat. Palermo, II. Ser 68, 237–246 (2019). https://doi.org/10.1007/s12215-018-0353-y

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