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Semi-Commutators of toeplitz operators on Ap(?)

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Journal of Mathematical Research and Exposition 2004年第1期24卷 7-12页

作者：于涛孙善利浙江师范大学数学系浙江金华321004 北京航空航天大学应用数学系北京100083

In this paper, we investigate the semi-commutators of toeplitz operators on the weighted Bergman spaces Ap(?), and characterize the bounded harmonic functions u and v on the unit disk for which the semi-commutator of ... 详细信息

关键词： weighted Bergman space toeplitz operator semi-commutator harmonic function.

Algebraic Properties of toeplitz operators on Discrete Commutative Groups

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Journal of Mathematical Research and Exposition 2008年第2期28卷 396-402页

作者： GUO Xun Xiang Department of Mathematics and Computer Science Gannan Normal University Jiangxi 341000 China

In this paper,a generalized toeplitz operator is defined and some of results about the classical toeplitz operator are *** particular,we obtain the necessary and sufficient condition for the product of two such toeplitz operators to still be toeplitz operator and the necessary and sufficient condition for such toeplitz operator to be normal ***,a necessary condition for two such toeplitz operators to be commutative is established.

关键词： discrete commutative group almost stable subset toeplitz operator hyponormal operator Hankle operator analytic toeplitz operator

Some results for operators on a model space

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Frontiers of Mathematics in China 2018年第2期13卷 287-300页

作者： Mehmet GURDAL Ulas YAMANCI Mubariz GARAYEV Suleyman Demirel University Department of Mathematics 32260 Isparta Turkey Suleyman Demirel University Department of Statistics 32260 Isparta Turkey Department of Mathematics College of Science King Saud University P. O. Box 2455Riyadh 11451 Saudi Arabia

We investigate some problems for truncated toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated toeplitz operators on the model space Kθ = H^2θθH^2 is studied. We study in terms of Berezin symbols invertibility of model operators. We also prove some results for the Berezin number of the truncated toeplitz operators. Moreover, we study some property for H2-functions in terms of noncyclicity of co-analytic toeplitz operators and hypercyclicity of model operators.

关键词： Reproducing kernel Hilbert space (RKHS) reproducing kernel,Berezin symbol Berezin number truncated toeplitz operator modeloperator toeplitz operator

The S_p Property of a kind of Hankel operators and toeplitz operators

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Journal of Mathematical Research and Exposition 2006年第1期26卷 14-18页

作者：张成国姚祖喜中央民族大学数学系北京100081

For two kind of MSebius invariant subspace A^α,d（D） and A^β,2 （D）, define the toeplitz operators Tf^s and Hankel operators Hf^r on A^α,d（D）×A^β,2 （D） with an arbi-trary analytic ＂symbol function＂ f on a... 详细信息

关键词： Moebius group weighted Bergman space toeplitz operator Hankel operator paracommutator Schatten-von Neumann property.

toeplitz and Hankel Products on Bergman Spaces of the Unit Ball

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Chinese Annals of Mathematics,Series B 2009年第3期30卷 293-310页

作者： Yufeng LU Chaomei LIU School of Mathematical Sciences Dalian University of Technology Dalian 116024 Liaoning China

The authors give some new necessary conditions for the boundedness of toeplitz products Tf^aTg^a on the weighted Bergman space Aa^2 of the unit ball, where f and g are analytic on the unit ball. Hankel products HfH9^＋ on the weighted Bergman space of the unit ball are studied, and the results analogous to those Stroethoff and Zheng obtained in the setting of unit disk are proved.

关键词： Weighted Bergman space Unit ball toeplitz operator Hankel operator Berezin transform

Sarason’s toeplitz Product Problem on the Fock–Sobolev Space

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Acta Mathematica Sinica,English Series 2018年第2期34卷 288-296页

作者： Jian Jun CHEN Xiao Feng WANG Jin XIA Guang Fu CAO School of Mathematics and Statistics Zhaoqing University Zhaoqing 526061 P. R. China School of Mathematics and Computational Science Sun Yat-sen University Guangzhou 510275 P. R. China School of Mathematics and Information Science and Key Laboratory of Mathematics andInterdisciplinary Sciences of the Guangdong Higher Education Institute Guangzhou University Guangzhou 510006 P. R. China College of Mathematics and Informatics South China Agricultural University Guangzhou 510642 P~ R. China

The Sarason＇s toeplitz product problem asks when the toeplitz product operator TuTv, with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the Fock-Sobolev space and have a complete solution that u = eq, v = Ce-q, where q is a linear complex polynomial and C is a nonzero constant.

关键词： Sarason's product toeplitz operator Berezin transform Fock Sobolev space

THE BEREZIN TRANSFORM AND ITS APPLICATIONS

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Acta Mathematica Scientia 2021年第6期41卷 1839-1858页

作者： Kehe ZHU Department of Mathematics and Statistics State University of New YorkAlbanyNY12222USA

We give a survey on the Berezin transform and its applications in operator theory. The focus is on the Bergman space of the unit disk and the Fock space of the complex plane. The Berezin transform is most effective an... 详细信息

关键词： reproducing kernel reproducing kernel Hilbert space Hardy space Bergman space Fock space Berezin transform toeplitz operator Hankel operator composition operator

Carleson Measures on the Weighted Bergman Spaces with Békollé Weights

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Chinese Annals of Mathematics,Series B 2021年第4期42卷 583-600页

作者： Cezhong TONG Junfeng LI Institute of Mathematics Hebei University of TechnologyTianjin 300401China Depaxtment of Mathematical Sciences Tsinghua UniversityBeijing 100084China

In this paper,the authors characterize Carleson measures for the weighted Bergman spaces with Békollé weights on the unit *** apply the Carleson embedding theorem to study the properties of toeplitz-type operators a... 详细信息

关键词： Békolléweight Bergman space Carleson measure toeplitz operator Composition operator

Commuting of toeplitz operators in Several Complex Variables

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Northeastern Mathematical Journal 2001年第3期17卷 253-256页

作者：卢玉峰孙善利 DepartmentofAppliedMathematics DalianUniversityofTechnologyDalian160024 CommunicatedbySunShanli

1 IntroductionLet Ω be the unit ball Bn or the polydisk Dn in Cn, and dA denote the Lebesgue measure on Ω, normalized so that the measure of Ω equals 1. L2a(Ω) is The Bergman space. For z ∈Ω, the Bergman reprodu... 详细信息

关键词： toeplitz operator commutant function of several complex variables