Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma"...In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.展开更多
Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrice...Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.展开更多
Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ...Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ with another one's adjoint C * ψ on the vector\|valued Bergman space B 1(X) for forms C φC * ψ and C * ψC φ.展开更多
Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give ...Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).展开更多
In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,...In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.展开更多
In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we es...In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter's and approximate essential spectrum.展开更多
Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger ...Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.展开更多
A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators ...A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.展开更多
Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear ...Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear operator L : M2n(F) → M2n(F) is said to preserve the symplectic group if L(SP2n(F)) = SP2n(F). It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form (i) L(X) = QPXP^-1 for any X ∈ M2n(F) or (ii) L(X) = QPX^TP^-1 for any X ∈M2n(F), where Q ∈ SP2n(F) and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3(1975), 715-724.展开更多
Inverse and saturation theorems have been studied for linear combination of some summation integral hybrid linear positive operators. Linear approximating technique and Steklov means have been used to obtain better ap...Inverse and saturation theorems have been studied for linear combination of some summation integral hybrid linear positive operators. Linear approximating technique and Steklov means have been used to obtain better approximation results.展开更多
Making use of a linear operator Iλp(a,c), which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion propertie...Making use of a linear operator Iλp(a,c), which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion properties of these subclasses. Some radius problems are also discussed.展开更多
In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators se...In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.展开更多
This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters. From these results, one can, to a large ext...This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters. From these results, one can, to a large extent, explain and control the stability of some objects in their moving processes.展开更多
A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exist...A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained.展开更多
In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we ob...In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.展开更多
In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the ...In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.展开更多
We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T ...We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T = BU, where B is a lower triangular plus-operator, U is a J-unitary operator. We apply the above factorization to the study of basical properties of relations (1), in particular, convexity and compactness of their images with respect to the weak operator topology. Obtained results we apply to the known Koenigs embedding problem, the Krein-Phillips problem of existing of invariant semidefinite subspaces for some families of plus-operators and to some other fields.展开更多
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.
文摘Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.
文摘Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ with another one's adjoint C * ψ on the vector\|valued Bergman space B 1(X) for forms C φC * ψ and C * ψC φ.
基金Supported by the National Natural Science Foundation of China(11161033)Supported by the Inner Mongolia Normal University Talent Project Foundation(RCPY-2-2012-K-036)+1 种基金Supported by the Inner Mongolia Normal University Graduate Research Innovation Foundation(CXJJS14053)Supported by the Inner Mongolia Autonomous Region Graduate Research Innovation Foundation(S20141013525)
文摘Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).
基金supported by the Natural Science Foundation of Guangdong Province(2021A1515010058)。
文摘In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.
文摘In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter's and approximate essential spectrum.
文摘Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.
文摘A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.
文摘Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear operator L : M2n(F) → M2n(F) is said to preserve the symplectic group if L(SP2n(F)) = SP2n(F). It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form (i) L(X) = QPXP^-1 for any X ∈ M2n(F) or (ii) L(X) = QPX^TP^-1 for any X ∈M2n(F), where Q ∈ SP2n(F) and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3(1975), 715-724.
文摘Inverse and saturation theorems have been studied for linear combination of some summation integral hybrid linear positive operators. Linear approximating technique and Steklov means have been used to obtain better approximation results.
文摘Making use of a linear operator Iλp(a,c), which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion properties of these subclasses. Some radius problems are also discussed.
文摘In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.
文摘This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters. From these results, one can, to a large extent, explain and control the stability of some objects in their moving processes.
文摘A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained.
基金The questions were posed during B. de Pagter was visiting the Queen's University of Belfast in Spring 1997, whilst the second author stayed at Belfast
文摘In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.
文摘In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.
基金This work was supported by Junta de Andalucia. Grupo de investigacion Matematica Aplioada. Codao 1107
文摘In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.
文摘We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T = BU, where B is a lower triangular plus-operator, U is a J-unitary operator. We apply the above factorization to the study of basical properties of relations (1), in particular, convexity and compactness of their images with respect to the weak operator topology. Obtained results we apply to the known Koenigs embedding problem, the Krein-Phillips problem of existing of invariant semidefinite subspaces for some families of plus-operators and to some other fields.