SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

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SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

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doi:10.1007/s10473-021-0301-3

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 657-669.doi: 10.1007/s10473-021-0301-3

• 论文 • 下一篇

陈泳¹, Kei Ji IZUCHI², Kou Hei IZUCHI³, Young Joo LEE⁴

1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;
2. Department of Mathematics, Niigata University, Niigata 950-2181, Japan;
3. Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi 753-8511, Japan;
4. Department of Mathematics, Chonnam National University, Gwangju 61186, Korea

收稿日期:2020-03-06 修回日期:2020-05-15 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Young Joo LEE E-mail:leeyj@chonnam.ac.kr
作者简介:Yong CHEN,E-mail:ychen227@gmail.com,ychen@hznu.edu.cn;Kei Ji IZUCHI,E-mail:izuchi@m.sc.niigata-u.ac.jp;Kou Hei IZUCHI,E-mail:izuchi@yamaguchi-u.ac.jp
基金资助:
The first author was supported by NSFC (11771401) and the last author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01041943).

Yong CHEN¹, Kei Ji IZUCHI², Kou Hei IZUCHI³, Young Joo LEE⁴

1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;
2. Department of Mathematics, Niigata University, Niigata 950-2181, Japan;
3. Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi 753-8511, Japan;
4. Department of Mathematics, Chonnam National University, Gwangju 61186, Korea

Received:2020-03-06 Revised:2020-05-15 Online:2021-06-25 Published:2021-06-07
Contact: Young Joo LEE E-mail:leeyj@chonnam.ac.kr
About author:Yong CHEN,E-mail:ychen227@gmail.com,ychen@hznu.edu.cn;Kei Ji IZUCHI,E-mail:izuchi@m.sc.niigata-u.ac.jp;Kou Hei IZUCHI,E-mail:izuchi@yamaguchi-u.ac.jp
Supported by:
The first author was supported by NSFC (11771401) and the last author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01041943).

摘要： We consider Toeplitz operators $T_u$ with symbol $u$ on the Bergman space of the unit ball, and then study the convergences and summability for the sequences of powers of Toeplitz operators. We first charactreize analytic symbols $\varphi$ for which the sequence $T^{*k}_\varphi f$ or $T^{k}_\varphi f$ converges to 0 or $\infty$ as $k\to\infty$ in norm for every nonzero Bergman function $f$ . Also, we characterize analytic symbols $\varphi$ for which the norm of such a sequence is summable or not summable. We also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result.

关键词: Bergman space, Toeplitz operator

Abstract: We consider Toeplitz operators $T_u$ with symbol $u$ on the Bergman space of the unit ball, and then study the convergences and summability for the sequences of powers of Toeplitz operators. We first charactreize analytic symbols $\varphi$ for which the sequence $T^{*k}_\varphi f$ or $T^{k}_\varphi f$ converges to 0 or $\infty$ as $k\to\infty$ in norm for every nonzero Bergman function $f$ . Also, we characterize analytic symbols $\varphi$ for which the norm of such a sequence is summable or not summable. We also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result.

Key words: Bergman space, Toeplitz operator

中图分类号:

47B35

陈泳, Kei Ji IZUCHI, Kou Hei IZUCHI, Young Joo LEE. SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE[J]. 数学物理学报(英文版), 2021, 41(3): 657-669.

Yong CHEN, Kei Ji IZUCHI, Kou Hei IZUCHI, Young Joo LEE. SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE[J]. Acta mathematica scientia,Series B, 2021, 41(3): 657-669.

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