SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

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

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

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).

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

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/Abstract

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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[3]	彭茹, 邢晓蕾, 江良英. POINTWISE MULTIPLICATION OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF Cⁿ[J]. 数学物理学报(英文版), 2019, 39(4): 1003-1016.
[4]	Jongrak LEE. HYPONORMALITY OF BLOCK TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES[J]. 数学物理学报(英文版), 2017, 37(6): 1695-1704.
[5]	黎深莲, 张学军, 徐思. THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL[J]. 数学物理学报(英文版), 2017, 37(2): 425-438.
[6]	闫成\|吐尔德别克. TOEPLITZ OPERATORS ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRA[J]. 数学物理学报(英文版), 2015, 35(1): 182-188.
[7]	陈志华, 江良美, 颜启明. AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES[J]. 数学物理学报(英文版), 2014, 34(4): 1145-1156.
[8]	任广斌, Uwe KAHLER. PSEUDOHYPERBOLIC METRIC AND UNIFORMLY DISCRETE SEQUENCES IN THE REAL UNIT BALL[J]. 数学物理学报(英文版), 2014, 34(3): 629-638.
[9]	张学军, 席利华, 范海霞, 李俊锋. ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN Cⁿ[J]. 数学物理学报(英文版), 2014, 34(3): 779-789.
[10]	谢佩珠, 曹广福. TOEPLITZ OPERATORS ON HEISENBERG GROUP[J]. 数学物理学报(英文版), 2013, 33(6): 1589-1597.
[11]	陈泽乾, 欧阳威. A LITTLEWOOD-PALEY TYPE THEOREM FOR BERGMAN SPACES[J]. 数学物理学报(英文版), 2013, 33(1): 150-154.
[12]	夏锦, 王晓峰, 曹广福. S_p-CLASS (0 <p < ∞) TOEPLITZ OPERATOR WITH UNBOUNDED SYMBOL ON DIRICHLET SPACE[J]. 数学物理学报(英文版), 2012, 32(5): 1919-1928.
[13]	江良英, 欧阳才衡. COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL[J]. 数学物理学报(英文版), 2011, 31(5): 1679-1693.
[14]	吕小芬, 胡璋剑. COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS[J]. 数学物理学报(英文版), 2011, 31(2): 468-476.
[15]	刘永民, 于燕燕. ON COMPACTNESS FOR ITERATED COMMUTATORS[J]. 数学物理学报(英文版), 2011, 31(2): 491-500.

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

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