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Zero products of Toeplitz operators on Reinhardt domains

Published online by Cambridge University Press:  08 April 2021

Željko Čučković
Affiliation:
Department of Mathematics & Statistics, University of Toledo, Toledo, OH43606, USA e-mail: [email protected]@utoledo.edu
Zhenghui Huo
Affiliation:
Department of Mathematics & Statistics, University of Toledo, Toledo, OH43606, USA e-mail: [email protected]@utoledo.edu
Sönmez Şahutoğlu*
Affiliation:
Department of Mathematics & Statistics, University of Toledo, Toledo, OH43606, USA e-mail: [email protected]@utoledo.edu

Abstract

Let $\Omega $ be a bounded Reinhardt domain in $\mathbb {C}^n$ and $\phi _1,\ldots ,\phi _m$ be finite sums of bounded quasi-homogeneous functions. We show that if the product of Toeplitz operators $T_{\phi _m}\cdots T_{\phi _1}=0$ on the Bergman space on $\Omega $ , then $\phi _j=0$ for some j.

Type
Article
Copyright
© Canadian Mathematical Society 2021

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