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Zero products of Toeplitz operators on Reinhardt domains

Part of: Holomorphic functions of several complex variables Special classes of linear operators

Published online by Cambridge University Press:  08 April 2021

Željko Čučković ,
Zhenghui Huo  and
Sönmez Şahutoğlu
Željko Čučković
Affiliation:
Department of Mathematics & Statistics, University of Toledo, Toledo, OH43606, USA e-mail: Zeljko.Cuckovic@utoledo.eduZhenghui.Huo@utoledo.edu
Zhenghui Huo
Affiliation:
Department of Mathematics & Statistics, University of Toledo, Toledo, OH43606, USA e-mail: Zeljko.Cuckovic@utoledo.eduZhenghui.Huo@utoledo.edu
Sönmez Şahutoğlu*
Affiliation:
Department of Mathematics & Statistics, University of Toledo, Toledo, OH43606, USA e-mail: Zeljko.Cuckovic@utoledo.eduZhenghui.Huo@utoledo.edu
*
e-mail: Sonmez.Sahutoglu@utoledo.edu
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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.

Keywords

Toeplitz operatorReinhardt domainBergman spacequasi-homogeneous

MSC classification

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Secondary: 32A36: Bergman spaces
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 170 - 179
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Copyright
© Canadian Mathematical Society 2021

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References

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