Essential Norm of Toeplitz Operators on Dirichlet-Type Spaces
Received:September 26, 2020  Revised:January 15, 2021
Key Word: Essential norm   Toeplitz operator   Dirichlet-type space  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.12001482), the Innovative Guidance Project of Science and Technology of Zhaoqing City (Grant No.202004031503), the Scientific Research Ability Enhancement Program for Excellent Young Teachers of Zhaoqing University (Grant No.ZQ202108), the Natural Research Project of Zhaoqing University (Grant No.221622) and the Innovative Research Team Project of Zhaoqing University.
Author NameAffiliation
Jianjun CHEN School of Mathematics and Statistics, Zhaoqing University, Guangdong 526061, P. R. China
School of Mathematics, Sun Yat-sen University, Guangdong 510275, P. R. China 
Jiesheng XIAO Nanhu College, Jiaxing University, Zhejiang 314001, P. R. China
School of Mathematics, Sun Yat-sen University, Guangdong 510275, P. R. China 
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Abstract:
      In this paper, we show that, on the Dirichlet-type space of unit disk, the essential norm of a noncompact Toeplitz operator equals its distance to the set of compact Toeplitz operators, and moreover, this distance is realized by infinitely many compact Toeplitz operators, which is analogous to the case of the weighted Bergman space.
Citation:
DOI:10.3770/j.issn:2095-2651.2021.04.007
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