Algebraic Properties of Toeplitz Operators with Radial Symbols on the Bergman Space of the Unit Ball
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- 作者：Ze-Hua Zhou and Xing-Tang Dong
- 关键词：Toeplitz operator ; Bergman space ; Mellin transform ; radial symbol ; quasihomogeneous symbol
- 刊名：Integral Equations and Operator Theory
- 出版年：2009
- 出版时间：May, 2009
- 年：2009
- 卷：64
- 期：1
- 页码：137-154
- 全文大小：269.3 KB
文摘
In this paper, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Bergman space of the unit ball in \mathbbCn{\mathbb{C}}^{n}. We first determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. Next, we investigate the zero-product problem for several Toeplitz operators with radial symbols. Also, the corresponding commuting problem of Toeplitz operators whose symbols are of the form xk j\xi^{k} \varphi is studied, where k ? \mathbbZnk \in {\mathbb{Z}}^{n} and φ is a radial function.