Berezin regularity of domains in ℂⁿ and the essential norms of Toeplitz operators,Transactions of the American Mathematical Society

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Berezin regularity of domains in ℂⁿ and the essential norms of Toeplitz operators
Transactions of the American Mathematical Society ( IF 1.3 ) Pub Date : 2021-01-26 , DOI: 10.1090/tran/8201
Željko Čučković , Sönmez Şahutoğlu

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.

中文翻译：

ez中的Berezin规则性和Toeplitz算子的基本范式

摘要：对于复平面中的开放单位圆盘，众所周知，如果它的Berezin变换也属于。我们说这是BC常规的。在本文中，我们研究了其中某些伪凸域的BC正则性，并证明边界几何起着重要作用。我们还建立了自然Toeplitz子代数中算子的基本范数与其Berezin变换之间的关系。 $\ mathbb {D}$ $\ phi \ in C（\ overline {\ mathbb {D}}）$ $\ widetilde {\ phi}$ $C（\ overline {\ mathbb {D}}）$ $\ mathbb {D}$ $\ mathbb {C} ^ n$

更新日期：2021-03-02

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