Essential Norm of Toeplitz Operators on Dirichlet-type space
Received:September 26, 2020  Revised:January 17, 2021
Key Word: Essential norm   Toeplitz operator   Dirichlet-type space  
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Jianjun Chen Zhaoqing University Zhaoqing University, Zhaoqing, China
Jiesheng Xiao Jiexing university 
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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.
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