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Toeplitz Operators with Positive Operator-Valued Symbols on Vector-Valued Generalized Fock Spaces

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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 \(F_\varphi^2\). Main results including Fock-Carleson condition, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten-p class are all considered.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, 526061, China

    Jianjun Chen  (陈建军)

  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

    Xiaofeng Wang  (王晓峰) & Jin Xia  (夏锦)

Authors
  1. Jianjun Chen  (陈建军)
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  2. Xiaofeng Wang  (王晓峰)
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  3. Jin Xia  (夏锦)
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Corresponding author

Correspondence to Xiaofeng Wang  (王晓峰).

Additional information

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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Chen, J., Wang, X. & Xia, J. Toeplitz Operators with Positive Operator-Valued Symbols on Vector-Valued Generalized Fock Spaces. Acta Math Sci 40, 625–640 (2020). https://doi.org/10.1007/s10473-020-0303-6

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  • DOI: https://doi.org/10.1007/s10473-020-0303-6

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