We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient ...We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function g_(w,s)∈(A_(α)^(2)(D))^(⊥),which is similar to the reproducing kernel of the weighted Bergman space A_(α)^(2)(D).We also give some additional applications of the function gw,s∈(A_(α)^(2)(D))^(⊥).展开更多
In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which ...In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which is a class of radial weights satisfying the two-sided doubling conditions.As an application,the bounded and compact positive Toeplitz operators T_(μ,ω)on the endpoint case weighted harmonic Bergman space L_(h,ω)^(1)(D)are characterized.展开更多
In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.
In this paper,we investigate the complex symmetric structure of Toeplitz operators T_(φ)on the Hardy space over the bidisk.We first characterize the weighted composition operators,W_(u,v)which are J-symmetric and uni...In this paper,we investigate the complex symmetric structure of Toeplitz operators T_(φ)on the Hardy space over the bidisk.We first characterize the weighted composition operators,W_(u,v)which are J-symmetric and unitary.As a consequence,we characterize conjugations of the form A_(u,v).In addition,a class of conjugations of the form C_(λ,a)is introduced.We show that the class of conjugations C_(λ,a)coincides with the class of conjugations A_(u,v);we then characterize the complex symmetry of the Toeplitz operators T_(φ)with respect to the conjugation C_(λ,a).展开更多
In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in...In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in the class of functions Ф=F ＋ G＊ withmatrix-valued polynomial functions F and G with degree 2.展开更多
The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that s...The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry.展开更多
We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of C^(n).Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type inte...We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of C^(n).Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^(p) to weighted Bergman spaces A_(α)^(q) for the different values of p and q in the unit ball.展开更多
In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz op...In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz operators. Then we obtain spectral properties of dual Toeplitz operators. Finally, we show that there are no quasinormal dual Toeplitz operators with bounded holomorphic or anti-holomorphic symbols.展开更多
In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz oper...In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonie Bergman space.展开更多
In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball Bn. First, we describe commutators of a radial Toeplitz operator and charac...In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball Bn. First, we describe commutators of a radial Toeplitz operator and characterize commuting Toeplitz operators with quasihomogeneous symbols. Then we show that finite raak product of such operators only happens in the trivial case. Finally, some necessary and sufficient conditions are given for the product of two quasihomogeneous Toeplitz operators to be a quasihomogeneous Toeplitz operator.展开更多
We prove a reverse HSlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk. Next, we further describe when for which square ...We prove a reverse HSlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk. Next, we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products TfTg are bounded invertible Toeplitz operators.展开更多
Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and o...Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.展开更多
In this paper,we introduce the harmonic Hardy space on Tn and study some algebraic properties of dual Toeplitz operator on the harmonic Hardy space on Tn.
Important operator characteristics (such boundedness or compactness) for particular classes of operators on particular reproducing kernel Hilbert spaces may be impacted by the behaviour of the operators on the reprodu...Important operator characteristics (such boundedness or compactness) for particular classes of operators on particular reproducing kernel Hilbert spaces may be impacted by the behaviour of the operators on the reproducing kernels. These results have been shown for Toeplitz operators on the Paley-Wiener space, a reproducing kernel Hilbert space over C. Furthermore, we show how the norm of such an operator has no relation to the supremum of the norms of the pictures of the normalization reproducing kernels of the space. As a result, if this supremum is finite, the operator is implicitly bounded. To further demonstrate that the operator norm is not the same as the supremum of the norms of the pictures of the real normalized reproducing kernels, another example is also provided. We also set out a necessary and sufficient condition for the operators’ compactness in terms of their limiting function on the reproducing kernels.展开更多
In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-c...In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-commutators of two Toeplitz operators with quasi- homogeneous symbols.展开更多
In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H^(2)(D) and the Fock space g^(2).The technique used to investigate the complex symmetry of unbounded Toeplitz operators is diff...In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H^(2)(D) and the Fock space g^(2).The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.展开更多
In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson ...In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.展开更多
Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm...Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.展开更多
In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of k1^th-order slant Toeplitz operators and k2^th-order slant Toeplitz operators must be a （klk2）^th-o...In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of k1^th-order slant Toeplitz operators and k2^th-order slant Toeplitz operators must be a （klk2）^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.展开更多
In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In additio...In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.展开更多
基金Supported by the Scientific Research Fund of Liaoning Provincial Education Department of China (Grant No.LJKMZ20221405)the National Natural Science Foundation of China (Grant No.12031002)。
文摘We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function g_(w,s)∈(A_(α)^(2)(D))^(⊥),which is similar to the reproducing kernel of the weighted Bergman space A_(α)^(2)(D).We also give some additional applications of the function gw,s∈(A_(α)^(2)(D))^(⊥).
基金supported by the National Natural Science Foundation of China(12171075)the Science and Technology Research Project of Education Department of Jilin Province(JJKH20241406KJ)Zhan’s research was supported by the Doctoral Startup Fund of Liaoning University of Technology(XB2024029).
文摘In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which is a class of radial weights satisfying the two-sided doubling conditions.As an application,the bounded and compact positive Toeplitz operators T_(μ,ω)on the endpoint case weighted harmonic Bergman space L_(h,ω)^(1)(D)are characterized.
基金supported by the Natural Science Foundation of China(12271134)the Shanxi Scholarship Council of China(2020–089)the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province(20200019).
文摘In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.
基金partially the National Natural Science Foundation of China(11771340,12101179,12171373)。
文摘In this paper,we investigate the complex symmetric structure of Toeplitz operators T_(φ)on the Hardy space over the bidisk.We first characterize the weighted composition operators,W_(u,v)which are J-symmetric and unitary.As a consequence,we characterize conjugations of the form A_(u,v).In addition,a class of conjugations of the form C_(λ,a)is introduced.We show that the class of conjugations C_(λ,a)coincides with the class of conjugations A_(u,v);we then characterize the complex symmetry of the Toeplitz operators T_(φ)with respect to the conjugation C_(λ,a).
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2009-0093827)
文摘In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in the class of functions Ф=F ＋ G＊ withmatrix-valued polynomial functions F and G with degree 2.
基金Supported by the National Natural Science Foundation of China (10371082)Chinese National Natural Science Foundation Committee Tianyuan Foundation (10526040)Guangzhou University Doctor Foundation (WXF-1001)
文摘The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry.
基金supported by the National Natural Science Foundation of China(11771441 and 11601400)。
文摘We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of C^(n).Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^(p) to weighted Bergman spaces A_(α)^(q) for the different values of p and q in the unit ball.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11501075,11271059)the Natural Science Foundation of Liaoning Education Department(Grant No.L2015084)the Natural Science Foundation of Guangxi Education Department(Grant No.KY2015LX518)
文摘In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz operators. Then we obtain spectral properties of dual Toeplitz operators. Finally, we show that there are no quasinormal dual Toeplitz operators with bounded holomorphic or anti-holomorphic symbols.
基金Supported by Innovation Program of Shanghai Municipal Education Commission(Grant No.13YZ090)
文摘In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonie Bergman space.
基金Supported by the National Natural Science Foundation of China (Grant No.11271059)
文摘In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball Bn. First, we describe commutators of a radial Toeplitz operator and characterize commuting Toeplitz operators with quasihomogeneous symbols. Then we show that finite raak product of such operators only happens in the trivial case. Finally, some necessary and sufficient conditions are given for the product of two quasihomogeneous Toeplitz operators to be a quasihomogeneous Toeplitz operator.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971020)
文摘We prove a reverse HSlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk. Next, we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products TfTg are bounded invertible Toeplitz operators.
基金Supported by Doctoral Program Foundation of Higher Education.
文摘Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1167106511301047)
文摘In this paper,we introduce the harmonic Hardy space on Tn and study some algebraic properties of dual Toeplitz operator on the harmonic Hardy space on Tn.
文摘Important operator characteristics (such boundedness or compactness) for particular classes of operators on particular reproducing kernel Hilbert spaces may be impacted by the behaviour of the operators on the reproducing kernels. These results have been shown for Toeplitz operators on the Paley-Wiener space, a reproducing kernel Hilbert space over C. Furthermore, we show how the norm of such an operator has no relation to the supremum of the norms of the pictures of the normalization reproducing kernels of the space. As a result, if this supremum is finite, the operator is implicitly bounded. To further demonstrate that the operator norm is not the same as the supremum of the norms of the pictures of the real normalized reproducing kernels, another example is also provided. We also set out a necessary and sufficient condition for the operators’ compactness in terms of their limiting function on the reproducing kernels.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1127105911301047)the Scientific Research Found of Higher School of Inner Mongolia(Grant No.NJZY 13298)
文摘In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-commutators of two Toeplitz operators with quasi- homogeneous symbols.
基金partially supported by the National Natural Science Foundation of China(11771340)。
文摘In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H^(2)(D) and the Fock space g^(2).The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.
基金Supported by National Natural Science Foundation of China(11471084,11301101,11971125)Young Innovative Talent Project of Department of Edcucation of Guangdong Province(2017KQNCX220)the Natural Research Project of Zhaoqing University(221622).
文摘In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.
基金partly supported by Natural Science Foundation of the Xinjiang Uygur Autonomous Region(2013211A001)
文摘Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1127105911226120)
文摘In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of k1^th-order slant Toeplitz operators and k2^th-order slant Toeplitz operators must be a （klk2）^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.
基金Supported by the National Natural Science Foundation of China(Grant No.11271092)the Natural Science Foundation of Guangdong Province(Grant No.S2011010005367)
文摘In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.
