## Berezin regularity of domains in $\mathbb {C}^n$ and the essential norms of Toeplitz operators

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- by Željko Čučković and Sönmez Şahutoğlu PDF
- Trans. Amer. Math. Soc.
**374**(2021), 2521-2540 Request permission

## Abstract:

For the open unit disc $\mathbb {D}$ in the complex plane, it is well known that if $\phi \in C(\overline {\mathbb {D}})$ then its Berezin transform $\widetilde {\phi }$ also belongs to $C(\overline {\mathbb {D}})$. We say that $\mathbb {D}$ is BC-regular. In this paper we study BC-regularity of some pseudoconvex domains in $\mathbb {C}^n$ and show that the boundary geometry plays an important role. We also establish a relationship between the essential norm of an operator in a natural Toeplitz subalgebra and its Berezin transform.## References

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## Additional Information

**Željko Čučković**- Affiliation: Department of Mathematics & Statistics, University of Toledo, Toledo, Ohio 43606
- MR Author ID: 294593
- Email: Zeljko.Cuckovic@utoledo.edu
**Sönmez Şahutoğlu**- Affiliation: Department of Mathematics & Statistics, University of Toledo, Toledo, Ohio 43606
- ORCID: 0000-0003-0490-0113
- Email: Sonmez.Sahutoglu@utoledo.edu
- Received by editor(s): September 19, 2019
- Received by editor(s) in revised form: April 1, 2020, and April 27, 2020
- Published electronically: January 26, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**374**(2021), 2521-2540 - MSC (2020): Primary 47B35; Secondary 32W05
- DOI: https://doi.org/10.1090/tran/8201
- MathSciNet review: 4223024