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

doi:10.1007/s10473-020-0303-6

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 625-640.doi: 10.1007/s10473-020-0303-6

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

陈建军¹, 王晓峰², 夏锦²

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

收稿日期:2018-08-12 修回日期:2019-12-26 出版日期:2020-06-25 发布日期:2020-07-17
通讯作者: Xiaofeng WANG E-mail:wxf@gzhu.edu.cn
作者简介:Jianjun CHEN,E-mail:chenarmy@foxmail.com;Jin XIA,E-mail:xiaj@cdut.edu.cn
基金资助:
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).

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

Jianjun CHEN¹, Xiaofeng WANG², Jin XIA²

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).

摘要/Abstract

摘要： 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.

关键词: Toeplitz operator, operator-valued symbol, generalized Fock space

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

中图分类号:

47B32

陈建军, 王晓峰, 夏锦. TOEPLITZ OPERATORS WITH POSITIVE OPERATOR-VALUED SYMBOLS ON VECTOR-VALUED GENERALIZED FOCK SPACES[J]. 数学物理学报(英文版), 2020, 40(3): 625-640.

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.

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

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

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