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

Jianjun CHEN; Xiaofeng WANG; Jin XIA

doi:10.1007/s10473-020-0303-6

Acta mathematica scientia, Series B >

2020 , Vol. 40 >Issue 3: 625 - 640

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

Articles

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

Jianjun CHEN ,
Xiaofeng WANG ,
Jin XIA

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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 date: 2018-08-12

Revised date: 2019-12-26

Online published: 2020-07-17

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 F_ψ². 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

Cite this article

Jianjun CHEN , Xiaofeng WANG , Jin XIA . TOEPLITZ OPERATORS WITH POSITIVE OPERATOR-VALUED SYMBOLS ON VECTOR-VALUED GENERALIZED FOCK SPACES[J]. Acta mathematica scientia, Series B, 2020 , 40(3) : 625 -640 . DOI: 10.1007/s10473-020-0303-6

References

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