一类截断Hankel算子的复对称性

Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (4): 961-968.

Complex Symmetry for a Class of Truncated Hankel Operators

Liling Lai¹(),Jinjin Liang¹(),Yong Chen^2,*()

¹ College of Mathematics and Computer Science, Zhejiang Normal University, Zhejiang Jinhua 321004
² College of Mathematics, Hangzhou Normal University, Hangzhou 311121

Received:2021-10-26 Online:2022-08-26 Published:2022-08-08
Contact: Yong Chen E-mail:2680634507@qq.com;861776003@qq.com;ychen@hznu.edu.cn
Supported by:
the NSFC(11771401)

Abstract

Abstract:

The truncated Hankel operator is the compression to the model space of Hankel operator on the Hardy space. In this paper, the complex symmetry for a class of truncated Hankel operators is studied and the complete characterization is given. The obtained results show that, the complex symmetry of truncated Hankel operator may be related to the model space only, or to the model space and the symbol function of the operator both.

Key words: Hankel operator, Model space, Complex symmetry, Finite Blaschke product

CLC Number:

O177.1

Liling Lai,Jinjin Liang,Yong Chen. Complex Symmetry for a Class of Truncated Hankel Operators[J].Acta mathematica scientia,Series A, 2022, 42(4): 961-968.

Trendmd

References 16

1	Ahern P , $\breve{\rm C}$u$\breve{\rm c}$kovi$\acute{\rm c}$ $\breve{\rm Z}$ . A theorem of Brown-Halmos type for Bergman space Toeplitz operators. J Funct Anal, 2001, 187: 200- 210 doi: 10.1006/jfan.2001.3811
2	Brown A , Halmos P R . Algebraic properties of Toeplitz operator. J Reine Angew Math, 1964, 213: 89- 102
3	Chen Y , Lee Y J , Zhao Y L . Complex symmetry of Toeplitz operators. Banach J Math Appl, 2022, 16: 15 doi: 10.1007/s43037-021-00171-5
4	Gao Y , Zhou Z H . Complex symmetric composition operators induced by linear fractional maps. Indiana Univ Math J, 2020, 69: 367- 384 doi: 10.1512/iumj.2020.69.7622
5	Garcia S R , Putinar M . Complex symmetric operators and applications. Trans Am Math Soc, 2006, 358: 1285- 1315
6	Garcia S R , Wogen W R . Complex symmetric partial isometries. J Funct Anal, 2009, 257: 1251- 1260 doi: 10.1016/j.jfa.2009.04.005
7	Gu C. Algebraic Properties of Truncated Hankel Operators. Preprint
8	Jurasik J , Lanucha B . Asymmetric truncated Toeplitz operators equal to the zero operator. Ann Univ Mariae Curie-Sklodowska Sect A, 2016, 70: 51- 62
9	Kang D , Kim H J . Products of truncated Hankel operators. J Math Anal Appl, 2016, 435: 1804- 1811 doi: 10.1016/j.jmaa.2015.11.019
10	Ko E , Lee J E . On complex symmetric Toeplitz operators. J Math Anal Appl, 2016, 434: 20- 34 doi: 10.1016/j.jmaa.2015.09.004
11	Li R , Yang Y X , Lu Y F . A class of complex symmetric Toeplitz operators on Hardy and Bergman spaces. J Math Anal Appl, 2020, 489 (2): 124173
12	Martinez-Avendano R . When do Toeplitz and Hankel operators commute?. Integr Equ Oper Theory, 2000, 37: 341- 349
13	Sarason D . Algebraic properties of truncated Toeplitz operators. Oper Matrices, 2007, 1: 491- 526
14	Sedlock N . Algebras of truncated Toeplitz operators. Oper Matrices, 2011, 5: 309- 326
15	Wang M F , Han K . Complex symmetric weighted composition operators in several variables. J Math Anal Appl, 2019, 474: 961- 987
16	Zhu S , Li C G . Complex symmetric weighted shifts. Trans Amer Math Soc, 2013, 365: 511- 530

[1]	Xia Jin, Wang Xiaofeng, Cao Guangfu. Bounded, Compact and Fredholm Toeplitz Operators on Harmonic Dirichlet Space D_h¹ [J]. Acta mathematica scientia,Series A, 2015, 35(5): 956-969.
[2]	XIA Jin, WANG Xiao-Feng, CAO Guang-Fu. Compact Operators on Dirichlet Space [J]. Acta mathematica scientia,Series A, 2009, 29(5): 1196-1205.
[3]	LIU Yong-Min. Schatten Class of Small Hankel Operators \=on Weighted Bergman Spaces [J]. Acta mathematica scientia,Series A, 2004, 24(3): 375-380.

Complex Symmetry for a Class of Truncated Hankel Operators

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 16

Related Articles 3

Metrics

Comments

Recommended 10