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arXiv · 1909.09221

Berezin regularity of domains in C^n and the essential norms of Toeplitz operators

Zeljko Cuckovic·Sonmez Sahutoglu
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Abstract

For the open unit disc $\mathbb{D}$ in the complex plane, it is well known that if $ϕ\in C(\overline{\mathbb{D}})$ then its Berezin transform $\widetildeϕ$ 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.

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Zeljko Cuckovic, Sonmez Sahutoglu. 2021-01-19. Berezin regularity of domains in C^n and the essential norms of Toeplitz operators. https://doi.org/10.1090/tran%2F8201

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