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Algebraic Properties of toeplitz and Small Hankel operators on the Harmonic Bergman Space

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Acta Mathematica Sinica,English Series 2014年第8期30卷 1395-1406页

作者： Hong Yan GUAN Yu Feng LU School of Mathematical Sciences Dalian University of Technology School of Mathematics and Systems Science Shenyang Normal University

In this paper,we discuss some algebraic properties of toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane *** solve the product problem of quasihomogeneous toeplitz operator and quasihomogeneous small Hankel ***,we characterize the commutativity of quasihomogeneous toeplitz operator and quasihomogeneous small Hankel operator.

关键词： toeplitz operator small Hankel operator quasihomogeneous symbols harmonic Bergman space Mellin transform

operators on Differential Form Spaces for Riemann Surfaces

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Acta Mathematica Sinica,English Series 2007年第5期23卷 925-934页

作者： Guang Fu CAO Xiao Feng WANG Department of Mathematics Guangzhou University Guangzhou 510405 P. R. China

In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator Cp is Predholm if and only if it is invertible if and only if p is invertible for some special cases. In addition, the toeplitz operators on ∧1 2, a（M） for Riemann surface M are defined and some properties of these operators are discussed.

关键词： Riemann surface Composition operator toeplitz operator

Localization of toeplitz operators on Bergman Spaces

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Northeastern Mathematical Journal 2001年第4期17卷 461-468页

作者：卢玉峰 Department of Applied Mathematics Dalian University of Technology Dalian 116024

In this paper we characterize the essential spectra of toeplitz operators on Bergman spaces by using Douglas’ localization Theorem and obtain the local decomposition of the essential spectra of toeplitz operators.

关键词： toeplitz operator Predholm operator fiber localization

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

L^pa（Bn）上toeplitz算子的等距同构

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Northeastern Mathematical Journal 1997年第3期13卷 299-302页

作者：丁宣浩 541004 Guilin Institute of Electronic Technology

For 1toeplitz operators Tf and Tg on is isometrically isomorphic if and only if there is a ψ∈Aut(B), such that g(z)

关键词： Bergman Space toeplitz operator Isometric Isomorphism

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广义toeplitz算子的代数性质

Northeastern Mathematical Journal 1999年第4期15卷 455-458页

作者：钟昌勇曹广福

In the present note, we discuss the algebraic properties of generalized toeplitz operators which satisfy the operator equation U *XU=λX, and partially solve a problem posed by Barria,J. and Halmos,P.R..

关键词： toeplitz operator Generalized toeplitz operator Hardy Space

Commutators of toeplitz operators On A^p(ψ)

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Northeastern Mathematical Journal 2000年第3期16卷 253-256页

作者：于涛孙善利卢玉峰孙顺华 DepartmentofMathematics JilinUniversityChangchun.130023 DepartmentofMathematics NortheasternNormalUniversity.Changchun130024

Let (ψ)denote the positive continous function on [0,1],(ψ) be called normal,if there exist two constants a and b(0＜a＜b)such that (ψ)(t)/(1-t2)ndecreases and (ψ)(t)/(1-t2)bincreaxes on[0,1],Let dm denote the norm... 详细信息

关键词： weighted Bergman space toeplitz operator commutator harmonic function

operators on the orthogonal complement of the Dirichlet space (Ⅱ)

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Science China Mathematics 2011年第9期54卷 2005-2012页

作者： YU Tao Department of Mathematics Zhejiang Normal University Jinhua 321004 China

In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞（D）, and then that a semicommutator of two toeplitz operators on the Dirichlet space or two dual toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact. We also prove that a dual Hankel operator Re with φ ∈ W^1,∞（D） is of finite rank if and only if Be is orthogonal to the Dirichlet space for some finite Blaschke product B, and give a sufficient and necessary condition for the semicommutator of two dual toeplitz operators to be of finite rank.

关键词： Sobolev space Dirichlet space dual toeplitz operator dual Hankel operator toeplitz operator

Analytic toeplitz algebras and the Hilbert transform associated with a subdiagonal algebra

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Science China Mathematics 2014年第3期57卷 579-588页

作者： JI GuoXing College of Mathematics and Information Science Shaanxi Normal University

Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated with M, we consider toeplitz operators and the Hilbert transform associated with 8i. We prove that the commutant of left analytic toeplitz algebra on noncommutative Hardy space H2（A4） is just the right analytic toeplitz algebra. Furthermore, the Hilbert transform on noncommutative LP（Yt4） is shown to be bounded for 1 （ p （ ce. As an application, we consider a noncomnmtative analog of the space BMO and identify the dual space of noncommutative Hl（M） as a concrete space of operators.

关键词： von Neumann algebra subdiagonal algebra noncommutative Hp space toeplitz operator Hilbert transform