Advertisement

Integral Equations and Operator Theory

, Volume 64, Issue 1, pp 137–154 | Cite as

Algebraic Properties of Toeplitz Operators with Radial Symbols on the Bergman Space of the Unit Ball

  • Ze-Hua Zhou
  • Xing-Tang Dong
Article

Abstract.

In this paper, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Bergman space of the unit ball in \({\mathbb{C}}^{n}\). 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 \(\xi^{k} \varphi\) is studied, where \(k \in {\mathbb{Z}}^{n}\) and φ is a radial function.

Mathematics Subject Classification (2000).

Primary 47B35 Secondary 32A36 

Keywords.

Toeplitz operator Bergman space Mellin transform radial symbol quasihomogeneous symbol 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsTianjin UniversityTianjinP.R. China

Personalised recommendations