Compact Toeplitz operators on the weighted Dirichlet space

2014 ◽  
Vol 31 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Yu Feng Lu ◽  
Yin Yin Hu ◽  
Liu Liu
Keyword(s):  
Toeplitz Operators ◽  
Dirichlet Space ◽  
Weighted Dirichlet Space

Kernels and spectrum of Toeplitz operators on the Dirichlet space

2019 ◽  
Vol 472 (1) ◽  
pp. 894-919 ◽  
Author(s):  
Yongning Li ◽  
Ziliang Zhang ◽  
Dechao Zheng
Keyword(s):  
Toeplitz Operators ◽  
Dirichlet Space

scholarly journals Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yinyin Hu ◽  
Yufeng Lu ◽  
Tao Yu
Keyword(s):  
Sobolev Space ◽  
Unit Ball ◽  
Toeplitz Operators ◽  
Dirichlet Space ◽  
Orthogonal Complement ◽  
Pluriharmonic Functions

We completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, forfandgpluriharmonic functions,SfSg=SgSfon(Dh)⊥if and only iffandgsatisfy one of the following conditions:(1)bothfandgare holomorphic;(2)bothf¯andg¯are holomorphic;(3)there are constantsαandβ, both not being zero, such thatαf+βgis constant.

scholarly journals On the closed range problem for composition operators on the Dirichlet space

2019 ◽  
Vol 6 (1) ◽  
pp. 76-81
Author(s):  
Nina Zorboska
Keyword(s):  
Toeplitz Operators ◽  
Composition Operators ◽  
Dirichlet Space ◽  
Closed Range ◽  
Berezin Transforms

Abstract We characterize closed range composition operators on the Dirichlet space for a particular class of composition symbols. The characterization relies on a result about Fredholm Toeplitz operators with BMO1 symbols, and with Berezin transforms of vanishing oscillation.

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