Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the B...Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the Berezin transform S(z) of S tends to zero as z→Ω.展开更多
In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ (...In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ ( m ) ) and e r ∞ (△ ( m ) ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.展开更多
It is proven that there exists a Dedekind complete Banach lattice E such that the linear spans/f (E) and IV (E) of positive compact and positive weakly compact operators on E fails to possess the Riesz separation ...It is proven that there exists a Dedekind complete Banach lattice E such that the linear spans/f (E) and IV (E) of positive compact and positive weakly compact operators on E fails to possess the Riesz separation property.展开更多
There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent result...There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent results in this area.展开更多
For a compact operator tuple A, if its projective spectrum P(A*) is smooth, then there exists a natural Hermitian holomorphic line bundle EAover P(A*) which is a unitary invariant for A. This paper shows that under so...For a compact operator tuple A, if its projective spectrum P(A*) is smooth, then there exists a natural Hermitian holomorphic line bundle EAover P(A*) which is a unitary invariant for A. This paper shows that under some additional spectral conditions, EAis a complete unitary invariant, i.e., EAcan determine the compact operator tuple up to unitary equivalence.展开更多
This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces. Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions fo...This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces. Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions for composition operator sequences to be collectively compact between weighted Bergman spaces are given展开更多
Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz opera...Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO(R^n) function and T~α.展开更多
In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators....In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω.展开更多
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
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 investigate the asymptotic spectrum and accumulation of a transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium. In L^p (1 ≤ p 〈 +∞) space...In this paper we investigate the asymptotic spectrum and accumulation of a transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium. In L^p (1 ≤ p 〈 +∞) space we show a series of new results for the asymptotic point spectrum and accumulation of A.展开更多
When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and...When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and compactness of composition operators from the space B0 to QK and QK,0.展开更多
Properties of composition operators induced by analytic self-maps on the unit disk of the complex plane in Hardy-Orlicz spaces are discussed. Results are concerned about boundedness, invertibility, compactness, Fredho...Properties of composition operators induced by analytic self-maps on the unit disk of the complex plane in Hardy-Orlicz spaces are discussed. Results are concerned about boundedness, invertibility, compactness, Fredholm operators and spectra of composition operators.展开更多
If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ 〈 ρ≤ 1). In this paper, we use a spec...If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ 〈 ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.展开更多
In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(...In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(compact)from one Dirichlet-type space,Da,into another one,D_(β).展开更多
Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known...Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.展开更多
In this paper, we study the compactness of the product of a composition operator with another one's adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given.
The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extr...The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.展开更多
Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces.The Grunsky map is known to be holomorphic on the universal Teichmüller space.In this pa...Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces.The Grunsky map is known to be holomorphic on the universal Teichmüller space.In this paper the authors deal with the compactness of a Grunsky differential operator.They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.展开更多
In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the a...In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.展开更多
文摘Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the Berezin transform S(z) of S tends to zero as z→Ω.
基金supported by the research project#144003 of the Serbian Ministry of Science, Technology and Development
文摘In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ ( m ) ) and e r ∞ (△ ( m ) ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.
文摘It is proven that there exists a Dedekind complete Banach lattice E such that the linear spans/f (E) and IV (E) of positive compact and positive weakly compact operators on E fails to possess the Riesz separation property.
文摘There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent results in this area.
基金supported by National Natural Science Foundation of China(Grant No.11671078)。
文摘For a compact operator tuple A, if its projective spectrum P(A*) is smooth, then there exists a natural Hermitian holomorphic line bundle EAover P(A*) which is a unitary invariant for A. This paper shows that under some additional spectral conditions, EAis a complete unitary invariant, i.e., EAcan determine the compact operator tuple up to unitary equivalence.
基金This research is supported by the National Natural Science Foundation of China
文摘This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces. Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions for composition operator sequences to be collectively compact between weighted Bergman spaces are given
基金supported by the NNSF of China(11571306)supported by the NNSF of China(11271330 and 11671363)supported by the NNSF of China(11371370)
文摘Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO(R^n) function and T~α.
基金This work is supported by Visiting Scholar Foundation of Key Lab in Peking UniversityThe project supported by the Science and Technical Development Foundation of Fuzhou UniversityThe projcect supported by the Science and Technical Foundation to the E
文摘In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω.
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 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Foundation item: Zhejiang Provincial Natural Science Foundation (102002) of China.
文摘In this paper we investigate the asymptotic spectrum and accumulation of a transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium. In L^p (1 ≤ p 〈 +∞) space we show a series of new results for the asymptotic point spectrum and accumulation of A.
基金Foundation item: Supported by the Natural Science Foundation of China(10471039) Supported by the Natural Science Foundation of the Education Committee of Jiangsu Province of China(06KJD110175+1 种基金 07KJB110115) Supported by the Scientific Research Foundation of Xuzhou professional of Architectural Technologies(07JYA3-13) Acknowledgment The authors thank the referees and the editors for good advice on this paper. The second author also thanks professors Shaozong Yan and Xiaoman Chen for their encouragement and help while visiting in Fudan university.
文摘When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and compactness of composition operators from the space B0 to QK and QK,0.
文摘Properties of composition operators induced by analytic self-maps on the unit disk of the complex plane in Hardy-Orlicz spaces are discussed. Results are concerned about boundedness, invertibility, compactness, Fredholm operators and spectra of composition operators.
基金Supported by the Doctoral programme foundation of National Education Ministry of China
文摘If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ 〈 ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.
基金supported by National Natural Science Foundation of China(11501157)supported by National Natural Science Foundation of China(12061022)the foundation of Guizhou Provincial Science and Technology Department(20177337 and 20175726)。
文摘In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(compact)from one Dirichlet-type space,Da,into another one,D_(β).
基金supported by the National Natural Science Foundation of China(Grant No.11971403)the Natural Science Foundation of Fujian Province of China(Grant No.2019J01024)。
文摘Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.
基金supported by the National Natural Science Foundation of China(No.10401027)
文摘In this paper, we study the compactness of the product of a composition operator with another one's adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given.
文摘The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.
基金the National Natural Science Foundation of China(No.11631010)。
文摘Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces.The Grunsky map is known to be holomorphic on the universal Teichmüller space.In this paper the authors deal with the compactness of a Grunsky differential operator.They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.
基金The project supported by NNSF of China(10071080)
文摘In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.