COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

doi:10.1007/s10473-020-103-2

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 35-44.doi: 10.1007/s10473-020-103-2

COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

蒋操¹, 董兴堂², 周泽华²

1. School of Mathematics and Information Sciences, Nanchang Hangkong University, Nanchang 330063, China;
2. School of Mathematics, Tianjin University, Tianjin 300350, China

收稿日期:2019-03-12 修回日期:2019-05-08 出版日期:2020-02-25 发布日期:2020-04-14
通讯作者: Xingtang dong E-mail:dongxingtang@163.com,dongxingtang@tju.edu.cn
基金资助:
This work was supported in part by the National Natural Science Foundation of China (11201331; 11771323).

COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

Cao JIANG¹, Xingtang DONG², Zehua ZHOU²

1. School of Mathematics and Information Sciences, Nanchang Hangkong University, Nanchang 330063, China;
2. School of Mathematics, Tianjin University, Tianjin 300350, China

Received:2019-03-12 Revised:2019-05-08 Online:2020-02-25 Published:2020-04-14
Contact: Xingtang dong E-mail:dongxingtang@163.com,dongxingtang@tju.edu.cn
Supported by:
This work was supported in part by the National Natural Science Foundation of China (11201331; 11771323).

摘要/Abstract

摘要： In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.

关键词: complex symmetric operator, Toeplitz operator, Bergman space, pluriharmonic Bergman space

Abstract: In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.

Key words: complex symmetric operator, Toeplitz operator, Bergman space, pluriharmonic Bergman space

中图分类号:

47B35

蒋操, 董兴堂, 周泽华. COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL[J]. 数学物理学报(英文版), 2020, 40(1): 35-44.

Cao JIANG, Xingtang DONG, Zehua ZHOU. COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL[J]. Acta mathematica scientia,Series B, 2020, 40(1): 35-44.

参考文献

[1] Dong X T, Zhou Z H. Algebric properties of toeplitz operators with separately quasihomogeneous symbols on the bergman space of the unit ball. J Oper Theory, 2011, 66(1):193-207
[2] Dong X T, Zhou Z H. Separately quasihomogeneous Toeplitz operators on the Bergman space of the polydisk (in Chinese). Sci Sin Math, 2011, 41(1):69-80
[3] Dong X T, Zhu K. Commutators and semi-commutators of Toeplitz operators on the unit ball. Integr Equat Oper Theory, 2016, 86(2):271-300
[4] Ferreira M. Some notes on complex symmetric operators. arXiv:1709.08616
[5] Garcia S R, Poore D E. On the norm closure of the complex symmetric operators:compact operators and weighted shifts. J Funct Anal, 2013, 264(3):691-712
[6] Garcia S R, Putinar M. Complex symmetric operators and applications. Trans Amer Math Soc, 2006, 358(3):1285-1315
[7] Garcia S R, Putinar M. Complex symmetric operators and applications II. Trans Amer Math Soc, 2007, 359(8):3913-3931
[8] Garcia S R, Wogen W R. Complex symmetric partial isometries. J Funct Anal, 2009, 257(4):1251-1260
[9] Garcia S R, Wogen W R. Some new class of complex symmetric operators. Trans Amer Math Soc, 2010, 362(11):6065-6077
[10] Guo K, Zhu S. A canonical decomposition of complex symmetric operators. J Oper Theory, 2014, 72(2):529-547
[11] Jiang C, Zhou Z H, Dong X T. Commutator and semicommutator of two monomial-type Toeplitz operators on the unit polydisk. Complex Anal Oper Theory, 2019, 13(5):2095-2121
[12] Ko E, Lee J. On complex symmetric Toeplitz operators. J Math Anal Appl, 2016, 434(1):20-34
[13] Mleczko P, Szwedek R. Complex symmetric operators and interpolation. J Math Anal Appl, 2018, 462(1):210-215
[14] Shu Y L, Zhao X F. Positivity of Toepitz operators on harmonic Bergman space. Acta Math Sin, English Series, 2016, 32(2):175-186
[15] Waleed Noor S. Complex symmetry of Toeplitz operators with continuous symbols. Arch Math, 2017, 109:455-460
[16] Wang M, Yao X. Complex symmetry of weighted composition operators in several variables. Int J Math, 2016, 27(2):165-170
[17] Zhu K. Spaces of Holomorphic Functions in the Unit Ball. New York:Springer, 2005

COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	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.
[2]	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.
[3]	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.
[4]	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.
[5]	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.
[6]	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.
[7]	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.
[8]	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.
[9]	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.
[10]	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.
[11]	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.
[12]	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.
[13]	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.
[14]	王晓峰; 曹广福. GALERKIN-PETROV METHODS OF TOEPLITZ OPERATORS ON DIRICHLET SPACE[J]. 数学物理学报(英文版), 2007, 27(2): 308-316.
[15]	罗罗, 史济怀. THE COMPACTNESS OF A KIND OF GENERALIZED HANKEL OPERATORS ON THE BERGMAN SPACE OF THE UNIT BALL[J]. 数学物理学报(英文版), 2000, 20(4): 471-475.