We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of ...We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.展开更多
Abstract: We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss ...Abstract: We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.展开更多
In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. ...In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. At last, we define two special numerical radius operator spaces and which can be seen as a quantization of norm space E.展开更多
We completely characterize commutativity of S and Sψ on La2(Dn)⊥ for bounded pluriharmonic symbols and ψ on Dn, and prove that SSψ = Sψ if and only if is analytic or ψˉ is analytic.
Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversati...Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.展开更多
In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal...In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal.Then we obtain a necessary and sufficient condition for the dual Toeplitz operator S_(φ) with the symbol φ(z)=az^(n1zm1)+bz^(n2zm2)(n1,n2,m1,m2∈N and a,b∈C)to be hyponormal.Finally,we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a finite rank.展开更多
In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions fo...In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator.展开更多
In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators wi...In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ.展开更多
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...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 essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.展开更多
We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■...We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.展开更多
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...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.展开更多
In this paper,we characterize that the boundedness,compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space.This generalizes the corresponding res...In this paper,we characterize that the boundedness,compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space.This generalizes the corresponding results for dual Toeplitz operators on the orthogonal complement of the Bergman space due to Stroethoff and Zheng’s paper[Trans.Amer.Math.Soc.,354,2495–2520(2002)].展开更多
The sequence space bvp consisting of all sequences (xk) such that (xk -xk-1) belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55(1), 136-147(2003)]; where 1 ≤ p ≤ ...The sequence space bvp consisting of all sequences (xk) such that (xk -xk-1) belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55(1), 136-147(2003)]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg's classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.展开更多
In this paper we first prove that a dual Hankel operator R φ 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...In this paper we first prove that a dual Hankel operator R φ 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 R φ with φ∈ W 1,∞(D) is of finite rank if and only if B φ 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.展开更多
In a more recent paper, the second author has introduced a space |Cα|k as the set of all series by absolute summable using Cesaro matrix of order α 〉 -1. In the present paper we extend it to the absolute NSrlund ...In a more recent paper, the second author has introduced a space |Cα|k as the set of all series by absolute summable using Cesaro matrix of order α 〉 -1. In the present paper we extend it to the absolute NSrlund space |Np^θ|k taking Norlund matrix in place of Cesaro matrix, and also examine some topological structures, α-β-γ-duals and the Schauder base of this space. Further we characterize certain matrix operators on that space and determine their operator norms, and so extend some well-known results.展开更多
In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz oper...In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz operators products.The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.展开更多
基金supported by the NSFC(12271134,11771401)supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2019R1I1A3A01041943)。
文摘We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.
基金The NSF(11501136,11271092)of Chinathe Key Discipline Construction Project of Subject Groups Focus on Mathematics+1 种基金Information Science in the Construction Project(4601-2015)of the High-level University of Guangdong Provincethe Project(HL02-1517)for the New Talent of Guangzhou University
文摘Abstract: We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.
文摘In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. At last, we define two special numerical radius operator spaces and which can be seen as a quantization of norm space E.
基金Foundation item: Supported by the Science Foundation of Zhejiang Education Ha11(20040850)Acknowledgment The authors would like to thank the referee for his useful comment.
文摘We completely characterize commutativity of S and Sψ on La2(Dn)⊥ for bounded pluriharmonic symbols and ψ on Dn, and prove that SSψ = Sψ if and only if is analytic or ψˉ is analytic.
基金the National Natural Science Foundation of China (Nos. 10672040 and10372022)the Natural Science Foundation of Fujian Province of China (No. E0410008)
文摘Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.
基金Partially supported by NSFC(Grant No.11701052)the second author was partially supported by the Fundamental Research Funds for the Central Universities(Grant Nos.2020CDJQY-A039 and 2020CDJ-LHSS-003)。
文摘In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal.Then we obtain a necessary and sufficient condition for the dual Toeplitz operator S_(φ) with the symbol φ(z)=az^(n1zm1)+bz^(n2zm2)(n1,n2,m1,m2∈N and a,b∈C)to be hyponormal.Finally,we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a finite rank.
文摘In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator.
文摘In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10671028, 10971020)
文摘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 essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.
基金supported by National Natural Science Foundation of China(Grant Nos.10971020 and 1127059)Research Fund for the Doctoral Program of Higher Education of China
文摘We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.
基金Supported by NSFC(Grant Nos.11271059,11271332,11431011,11301047)NSF of Zhejiang Province(Grant Nos.LY14A010013,LY14A010021)Higher School Foundation of Inner Mongolia of China(Grant No.NJZY13298)
文摘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.
基金Supported by NSFC(Grant No.11701052)Fundamental Research Funds for the Central Universities(Grant Nos.106112017CDJXY100007,2020CDJQY-A039,2020CDJ-LHSS-003)。
文摘In this paper,we characterize that the boundedness,compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space.This generalizes the corresponding results for dual Toeplitz operators on the orthogonal complement of the Bergman space due to Stroethoff and Zheng’s paper[Trans.Amer.Math.Soc.,354,2495–2520(2002)].
文摘The sequence space bvp consisting of all sequences (xk) such that (xk -xk-1) belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55(1), 136-147(2003)]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg's classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.
基金supported by National Natural Science Foundation of China (Grant Nos.10971195 and 10771064)Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090689 and Y6110260)Zhejiang Innovation Project (Grant No. T200905)
文摘In this paper we first prove that a dual Hankel operator R φ 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 R φ with φ∈ W 1,∞(D) is of finite rank if and only if B φ 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.
基金Supported by Pamukkale University Scientific Research Pro jects Coordinatorship(Grant No.2014FBE061)
文摘In a more recent paper, the second author has introduced a space |Cα|k as the set of all series by absolute summable using Cesaro matrix of order α 〉 -1. In the present paper we extend it to the absolute NSrlund space |Np^θ|k taking Norlund matrix in place of Cesaro matrix, and also examine some topological structures, α-β-γ-duals and the Schauder base of this space. Further we characterize certain matrix operators on that space and determine their operator norms, and so extend some well-known results.
文摘In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz operators products.The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.