Skip to main content Accessibility help
×
Home
Hostname: page-component-768dbb666b-v9bzm Total loading time: 0.249 Render date: 2023-02-05T14:02:59.025Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

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: 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

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahern, P. and Čučković, Ž., A theorem of Brown–Halmos type for Bergman space Toeplitz operators. J. Funct. Anal. 187(2001), no. 1, 200210.10.1006/jfan.2001.3811CrossRefGoogle Scholar
Ahern, P. and Čučković, Ž., Some examples related to the Brown–Halmos theorem for the Bergman space. Acta Sci. Math. (Szeged) 70(2004), nos. 1–2, 373378.Google Scholar
Aleman, A. and Vukotić, D., Zero products of Toeplitz operators . Duke Math. J. 148(2009), no. 3, 373403.10.1215/00127094-2009-029CrossRefGoogle Scholar
Bauer, W. and Le, T., Algebraic properties and the finite rank problem for Toeplitz operators on the Segal–Bargmann space . J. Funct. Anal. 261(2011), no. 9, 26172640.CrossRefGoogle Scholar
Brown, A. and Halmos, P. R., Algebraic properties of Toeplitz operators . J. Reine Angew. Math. 213(1963), no. 64, 89102.Google Scholar
Çelik, M. and Zeytuncu, Y. E., Nilpotent Toeplitz operators on Reinhardt domains . Rocky Mountain J. Math. 46(2016), no. 5, 13951404.10.1216/RMJ-2016-46-5-1395CrossRefGoogle Scholar
Choe, B. and Koo, H., Zero products of Toeplitz operators with harmonic symbols . J. Funct. Anal. 233(2006), no. 2, 307334.CrossRefGoogle Scholar
Choe, B. R., Lee, Y. J., Nam, K. and Zheng, D., Products of Bergman space Toeplitz operators on the polydisk . Math. Ann. 337(2007), no. 2, 295316.CrossRefGoogle Scholar
Dong, X.-T. and Zhou, Z.-H., Algebraic properties of Toeplitz operators with separately quasihomogeneous symbols on the Bergman space of the unit ball . J. Operator Theory 66(2011), no. 1, 193207.Google Scholar
Le, T., Compact Hankel operators on generalized Bergman spaces of the polydisc . Integ. Equat. Operator Theory 67(2010), no. 3, 425438.10.1007/s00020-010-1788-5CrossRefGoogle Scholar
Remmert, R., Classical topics in complex function theory. Graduate Texts in Mathematics, 172, Springer-Verlag, New York, 1998, Translated from the German by Kay, Leslie.Google Scholar

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Zero products of Toeplitz operators on Reinhardt domains
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Zero products of Toeplitz operators on Reinhardt domains
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Zero products of Toeplitz operators on Reinhardt domains
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *