Zero products of Toeplitz operators on Reinhardt domains. Issue 1 (8th March 2022)

• Record Type: Journal Article
• Authors: Čučković, Željko; Huo, Zhenghui; Şahutoğlu, Sönmez
• Is Part Of: Canadian mathematical bulletin =. Volume 65:Issue 1(2022)
• Page Start: 170
• Page End: 179
• Publication Date: 2022-03-08
• Subjects: 47B35 -- 32A36; Toeplitz operator -- Reinhardt domain -- Bergman space -- quasi-homogeneous; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/S0008439521000187
• Languages: English
• ISSNs: 0008-4395

Abstract

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 .