Essential Norm of Toeplitz Operators on the Fock Spaces

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• 作者：Zhangjian Hu ; Jin Lu
• 关键词：Primary 47B38 ; Secondary 32A36 ; 47G10 ; Toeplitz operator ; Hankel operator ; Fock space ; Essential norm
• 刊名：Integral Equations and Operator Theory
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：83
• 期：2
• 页码：197-210
• 全文大小：548 KB
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• 作者单位：Zhangjian Hu (1)
  Jin Lu (1)
  
  1. Department of Mathematics, Huzhou University, Huzhou, 313000, Zhejiang, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989

文摘

In this paper, we show that, on the generalized Fock space \({F^p(\varphi)}\) with \({1 < p < \infty}\) , the essential norm of a noncompact Toeplitz operator \({T_\mu}\) with \({|\mu|}\) being a Fock–Carleson measure equals its distance to the set of compact Toeplitz operators. Moreover, the distance is realized by infinitely many compact Toeplitz operators. Our approach is also available on the Bergman space setting. Keywords Toeplitz operator Hankel operator Fock space Essential norm