Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (3): 625-640.doi: 10.1007/s10473-020-0303-6

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TOEPLITZ OPERATORS WITH POSITIVE OPERATOR-VALUED SYMBOLS ON VECTOR-VALUED GENERALIZED FOCK SPACES

Jianjun CHEN1, Xiaofeng WANG2, Jin XIA2   

  1. 1 School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China;
    2 School of Mathematics and Information Science and Key Laboratory of Mathematics and Interdisciplinary Sciences of the Guangdong Higher Education Institute, Guangzhou University, Guangzhou 510006, China
  • Received:2018-08-12 Revised:2019-12-26 Online:2020-06-25 Published:2020-07-17
  • Contact: Xiaofeng WANG E-mail:wxf@gzhu.edu.cn
  • Supported by:
    Supported by National Natural Science Foundation of China (11471084, 11301101, 11971125), Young Innovative Talent Project of Department of Edcucation of Guangdong Province (2017KQNCX220), and the Natural Research Project of Zhaoqing University (221622).

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Abstract: In this article, we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ2. Main results including Fock-Carleson condition, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten-p class are all considered.

Key words: Toeplitz operator, operator-valued symbol, generalized Fock space

CLC Number: 

  • 47B32
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