Properties of Toeplitz Operators on the Dirichlet Space Over the Ball

Authors
Hu, Yin Yin Lu, Yu Feng Liu, Liu
Citation
Hu, Yin Yin et al., Properties of Toeplitz Operators on the Dirichlet Space Over the Ball, Acta mathematica Sinica. English series (Print) , 35(10), 2019, pp. 1617-1628
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
35
Issue
10
Year of publication
2019
Pages
1617 - 1628
Database
ACNP
SICI code
Abstract
On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero.