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Banach space structure of weighted Fock-Sobolev spaces

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Frontiers of Mathematics in China 2016年第3期11卷 693-703页

作者： Li HE guangfu cao Institute of Mathematics Guangzhou University Guangzhou 510006 China Institute of Mathematics South China Agricultural University Guangzbon 510642 China

We discuss the Banach space structure of the fractional order weighted Fock-Sobolev spaces fPα,s, mainly include giving some growth estimates for Fock-Sobolev functions and approximating them by a sequence of ＇nice... 详细信息

关键词： weighted Fock-Sobolev space approximation

Products of Toeplitz and Hankel Operators on Fock-Sobolev Spaces

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Chinese Annals of Mathematics,Series B 2022年第3期43卷 401-416页

作者： Yiyuan ZHANG guangfu cao Li HE School of Mathematics and Information Science Guangzhou UniversityGuangzhou 510006China

In this paper,the authors investigate the boundedness of Toeplitz product T_(f)T_(g)and Hankel product H^(*)_(f)H_(g)on Fock-Sobolev space for f,g∈*** a result,the boundedness of Toeplitz operator T_(f)and Hankel ope... 详细信息

关键词： Toeplitz product Hankel product Fock-Sobolev space

The commutants of analytic Toeplitz operators for several complex variables

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Science China Mathematics 2010年第7期53卷 1873-1880页

作者： cao guangfu Huang Sui Guangzhou Univ Dept Math Guangzhou 510006 Guangdong Peoples R China

It is proved that if  is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed.

关键词： Toeplitz operator commutant of an operator

Toeplitz operators on H^2(iR)

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Science China Mathematics 2011年第9期54卷 1995-2004页

作者： XIE PeiZhu cao guangfu Department of Mathematics Sun Yat-sen University Guangzhou 510275 China Department of Mathematics Guangzhou University Guangzhou 510006 China

In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is *** addition,the characteristic equation of Toeplitz operators is obtaine... 详细信息

关键词： Toeplitz operator Hardy space Fredholm theory

Hardy-Sobolev spaces and their multipliers

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Science China Mathematics 2014年第11期57卷 2361-2368页

作者： cao guangfu HE Li Department of Mathematics Guangzhou University Department of Mathematics Sun Yat-sen University

In this paper,some properties of Hardy-Sobolev spaces are obtained. The multipliers on these spaces are defined,and our results show that the multiplier algebra is more complex than that on the classical Hardy spaces.... 详细信息

关键词： Hardy-Sobolev space dual space spectrum

Toeplitz operators on Fock-Sobolev spaces with positive measure symbols

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Science China Mathematics 2014年第7期57卷 1443-1462页

作者： WANG XiaoFeng cao guangfu XIA Jin School of Mathematics and Information Science and Key Laboratory of Mathematics and Interdisciplinary Sciences of the Guangdong Higher Education Institute Guangzhou University

We discuss Toeplitz operators on Fock-Sobolev space with positive measure *** FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz *** also give some equivalent conditions o... 详细信息

关键词： Fock-Sobolev space Toeplitz operator boundedness compactness Schatten p-class

Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball

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Frontiers of Mathematics in China 2017年第4期12卷 769-785页

作者： Jianjun CHEN Xiaofeng WANG Jin XIA guangfu cao School of Mathematics and Statistics Zhaoqing University Zhaoqing 526061 China School of Mathematics and Information Science and Key Laboratory of Mathematics andInterdisciplinary Sciences of the Cuangdong Higher Education Institute Guangzhou University Guangzhou 510006 China College of Mathematics and Informaties South China Agricultural UniversityGuangzhou 510642 China School of Mathematics and Computational Science Sun Yat-sen University Guangzhou 510275 China

The present paper mainly gives some applications of Berezin type symbols on the Diriehlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX ＋ XB - CX = D related to harmonic Toeplitz operators on the Dirichlet space. Especially, the invariant subspaces of Toeplitz operators are also considered.

关键词： Riccati equation Toeplitz operator Dirichlet space unit ball

TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES

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Chinese Annals of Mathematics,Series B 2002年第3期23卷 385-396页

作者： cao guangfu Department of Mathematics, Sichuan University, Chengdu 610064, China. Department of Mathematics Sichuan University Chengdu 610064 China

The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz *** particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.

关键词： Dirichlet space Toeplitz operator Toeplitz algebra

Toeplitz Operators with Unbounded Symbols on Segal-Bargmann Space

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Journal of Mathematical Research with Applications 2015年第3期35卷 237-255页

作者： Li HE guangfu cao Department of Mathematics Guangzhou University

In this paper,we construct a function φ in L2(Cn,d Vα) which is unbounded on any neighborhood of each point in Cnsuch that Tφ is a trace class operator on the SegalBargmann space H2(Cn,d Vα).In addition,we also ch... 详细信息

关键词： Segal-Bargmann space Toeplitz operator unbounded function Schatten class