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Completely Non-Normal toeplitz operators

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Journal of Mathematical Research and Exposition 2011年第4期31卷 727-734页

作者： Yah Yue SHI Yu Feng LU School of Mathematical Sciences Dalian University of Technology Liaoning 116024 P. R. China

In this paper, we show that the hyponormal toeplitz operator Tφ with trigonometric polynomial symbol φ is either normal or completely non-normal. Moreover, if Tφ is non-normal, then Tφ has a dense set of cyclic ve... 详细信息

关键词： toeplitz operator completely nononormal hyponormal cyclic.

Hyponormality of toeplitz operators on the Dirichlet Space

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Journal of Mathematical Research and Exposition 2011年第6期31卷 1057-1063页

作者： Qiao Fei LU Tao YU Department of Mathematics Zhejiang Normal UniversityZhejiang 321004P.R.China

In this paper,we prove that the necessary and sufficient condition for a toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,*** also prove that a toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.

关键词： toeplitz operator hyponormality Dirichlet space harmonic Dirichlet space

Commuting Hankel and toeplitz operators on the Hardy Space of the Bidisk

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Journal of Mathematical Research and Exposition 2010年第2期30卷 205-216页

作者： Yu Feng LU Bo ZHANG School of Mathematical Science Dalian University of Technology Liaoning 116024 P. R. China

In this paper, we characterize when the toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condit... 详细信息

关键词： Hankel operator toeplitz operator Hardy space bidisk commuting.

Commuting toeplitz operators with Harmonic Symbols on A^2(■,dμ)

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Communications in Mathematical Research 2009年第2期25卷 165-176页

作者： WANG CHUN-MEI Institute of Mathematics Jilin University Changchun 130012

For any given symmetric measure μ on the closed unit disk D, we apply the Berezin transform to characterizing semi-commuting and commuting toeplitz operators with bounded harmonic symbols on A2（D, dμ）.

关键词： symmetric measure toeplitz operator Berezin transform

Zero Products and Finite Rank of toeplitz operators on the Harmonic Bergman Space

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Journal of Mathematical Research with Applications 2017年第3期37卷 325-334页

作者： Qian DING Yinyin HU Liu LIU Yufeng LU School of Mathematical Sciences Dalian University of Technology Department of Mathematics Dalian Maritime University

We study zero product problem and finite rank of the Brown-Halmos type results involving products of toeplitz operators acting on the harmonic Bergman space. We use the Berezin transform and invariant Laplacian in thi... 详细信息

关键词： toeplitz operator finite rank harmonic Bergman space

Essential Norm of toeplitz operators on Dirichlet-Type Spaces

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Journal of Mathematical Research with Applications 2021年第4期41卷 393-400页

作者： Jianjun CHEN Jiesheng XIAO School of Mathematics and Statistics Zhaoqing University School of Mathematics Sun Yat-sen University Nanhu College Jiaxing University

In this paper, we show that, on the Dirichlet-type space of unit disk, the essential norm of a noncompact toeplitz operator equals its distance to the set of compact toeplitz operators, and moreover, this distance is realized by infinitely many compact toeplitz operators,which is analogous to the case of the weighted Bergman space.

关键词： Essential norm toeplitz operator Dirichlet-type space

Algebraic Properties of toeplitz operators on Cutoff Harmonic Bergman Space

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Journal of Mathematical Research with Applications 2020年第2期40卷 169-186页

作者： Jingyu YANG Yufeng LU Huo TANG College of Mathematics and Computer Science Chifeng University School of Mathematical Sciences Dalian University of Technology

In this paper, we first investigate the finite-rank product problems of several toeplitz operators with quasihomogeneous symbols on the cutoff harmonic Bergman space b;. Next,we characterize finite rank commutators an... 详细信息

关键词： toeplitz operator Cutoff Harmonic Bergman space quasihomogeneous finite rank

Algebraic Properties of Dual toeplitz operators on Harmonic Hardy Space over Polydisc

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Journal of Mathematical Research with Applications 2016年第6期36卷 703-710页

作者： Yufeng LU Fatemeh AZARI KEY Hewei YANG Liu LIU School of Mathematical Sciences Dalian University of Technology

In this paper,we introduce the harmonic Hardy space on T~n and study some algebraic properties of dual toeplitz operator on the harmonic Hardy space on T~n.

关键词： Hardy space toeplitz operator spectrum semi-commutative

Product and Commutativity of Slant toeplitz operators

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Journal of Mathematical Research with Applications 2013年第1期33卷 122-126页

作者： Chaomei LIU Yufeng LU School of Science Dalian Jiaotong University School of Mathematical Sciences Dalian University of Technology

In this paper, the product and commutativity of slant toeplitz operators are discussed. We show that the product of kth1-order slant toeplitz operators and kth2-order slant toeplitz operators must be a (k1k2) th-order slant toeplitz operator except for zero operators, and the commutativity and essential commutativity of two slant toeplitz operators with different orders are the same.

关键词： toeplitz operator slant toeplitz operator product commutativity.