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Reducing Subspaces of Toeplitz Operators Induced by a Class of Non-analytic Monomials over the Unit Ball

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1767-1777页

作者： Yan yue SHI Bo ZHANG Xu TANG yu feng lu School of Mathematical Sciences Ocean University of ChinaQingdao 266100P.R.China School of Mathematics and Information Sciences Yantai UniversityYantai 264005P.R.China School of Mathematical Sciences Space Engineering UniversityBeijing 101416P.R.China School of Mathematical Sciences Dalian University of TechnologyDalian 116024P.R.China

In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a ***,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)*** also give some interesting examples.

关键词： Reducing subspace operator-weighted shifts Toeplitz operator von Neumann algebra

Commuting Dual Toeplitz Operators on Weighted Bergman Spaces of the Unit Ball

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Acta Mathematica Sinica,English Series 2011年第9期27卷 1725-1742页

作者： yu feng lu Jun YANG School of Mathematical Sciences Dalian University of Technology Dalian 116024 P. R. China College of Arts and Science Shanghai Maritime University Shanghai 201303 P. R. China

In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and es... 详细信息

关键词： Dual Toeplitz operator unit ball weighted Bergman space commutativity

Radial Operators on the Weighted Bergman Spaces over the Polydisk

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Acta Mathematica Sinica,English Series 2019年第2期35卷 227-238页

作者： Ran LI yu feng lu School of Mathematical Sciences Dalian University of Technology

In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the(m, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its(0, λ)-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its(m, λ)-Berezin transform is a separately radial function.

关键词： Radial operators (m,λ)-Berezin transform weighted Bergman spaces Toeplitz operators

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

Commuting Dual Toeplitz Operators on the Polydisk

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Acta Mathematica Sinica,English Series 2007年第5期23卷 857-868页

作者： yu feng lu Shu Xia SHANG Department of Applied Mathematics Dalian University of Technology Dalian 116024 P. R. China

On the polydisk, the commutativity of dual Toeplitz operators is studied. We obtain characterizations of commuting dual Toeplitz operators, essentially commuting dual Toeplitz operators and essentially semi-commuting ... 详细信息

关键词： dual Toeplitz operators polydisk Bergman space commute maximal ideal space

Commuting Toeplitz Operators on the Hardy Space of the Polydisk

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Acta Mathematica Sinica,English Series 2015年第4期31卷 695-702页

作者： Ling Hui KONG yu feng lu School of Mathematical Sciences Dalian University of Technology

In this paper, we show that two Toeplitz operators Tf and Tg on the Hardy space of the polydisk can commute if and only if the Berezin transform of the commutator [Tf, Tg] is n-harmonic.

关键词： Commuting Toeplitz operators Hardy space polydisk Berezin transform

Hyponormal Toeplitz Operators on the Polydisk

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Acta Mathematica Sinica,English Series 2012年第2期28卷 333-348页

作者： yu feng lu Yan yue SHI School of Mathematical Sciences Dalian University of TechnologyDalian 116024P.R.China

By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of Toeplitz operators on the Hardy space of the polydisk.

关键词： Hyponormality Toeplitz operator Hankel operator polydisk block matrix representation

Commuting Dual Toeplitz Operators on the Harmonic Dirichlet Space

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Acta Mathematica Sinica,English Series 2016年第9期32卷 1099-1105页

作者： Jing yu YANG Yin Yin HU yu feng lu Tao yu School of Mathematical Statistics Chifeng University Chifeng 024000 P. R. China School of Mathematical Sciences Dalian University of Technology Dalian 116024 P. R. China

In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if and only if φ and ψ satisfy one of the following conditions：（1） Both φ and ψ are harmonic functions; （2） There exist complex constants α and β, not both O, such that φ = αφ＋β.

关键词： Dual Toeplitz operator harmonic Dirichlet space commutativity

Properties of Toeplitz Operators on the Dirichlet Space Over the Ball

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Acta Mathematica Sinica,English Series 2019年第10期35卷 1617-1628页

作者： Yin Yin HU yu feng lu Liu LIU Department of Mathematics Dalian Maritime UniversityDalian 116024P.R.China Department of Mathematics Dalian University of TechnologyDalian 116024P.R.China

On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero.

关键词： Toeplitz operator pluriharmonic symbols Dirichlet space