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Properties of Toeplitz Operators on the Dirichlet Space Over the Ball

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Indexed by:Journal Papers

Date of Publication:2019-10-01

Journal:ACTA MATHEMATICA SINICA-ENGLISH SERIES

Included Journals:SCIE

Volume:35

Issue:10

Page Number:1617-1628

ISSN No.:1439-8516

Key Words:Toeplitz operator; pluriharmonic symbols; Dirichlet space

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.

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