Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space. (4th March 2013)

• Record Type: Journal Article
• Authors: Yang, Jingyu; Liu, Liu; Lu, Yufeng
• Other Names: Vasilevski Nikolai M. Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2013(2013)
• Publication Date: 2013-03-04
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2013/578436
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols.