Integral Equations and Operator Theory

, Volume 64, Issue 1, pp 137–154

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

Article

DOI: 10.1007/s00020-009-1677-y

Cite this article as:
Zhou, ZH. & Dong, XT. Integr. equ. oper. theory (2009) 64: 137. doi:10.1007/s00020-009-1677-y

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 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

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

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