In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-di...In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-difference means are in the linear space l（p） defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l（u, v, p, △（m）） to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp（U, v, △（m）） （1 ≤ p 〈 ∞）.展开更多
In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _dua...In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _duals. The criterions of bounded sets in l 1(X) and l ∞(X ) with respect to the weak topologies generated by the σ _duals are obtained. Furthermore, a Schur type result and an automatic continuity theorem of matrix transformation are established.展开更多
In this paper, we discuss some basic properties of the Orlicz-Bochner sequence space l_M(X) and its subspace h_M(X). We present the equivalent definition of h_M(X), the sufficient and necessary conditions under which ...In this paper, we discuss some basic properties of the Orlicz-Bochner sequence space l_M(X) and its subspace h_M(X). We present the equivalent definition of h_M(X), the sufficient and necessary conditions under which l_^(M) (X) is complete, and l_M(X) and h_M(X) are separable respectively, and also give the sufficient condition that h_M(X) has a basis. All these results generalize the results for the classical Orlicz sequence spaces.展开更多
In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr）...In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr） is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N.展开更多
In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coeffi...In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.展开更多
In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces？∞, c and c0 according to a new matrix operator W which is obtained by matrix pr...In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces？∞, c and c0 according to a new matrix operator W which is obtained by matrix product.展开更多
This paper describes characteristics of (A p,α,l q) with 0【p≤1,α】0 and p≤q≤∞. As the corollaries, the characteristics of (A p,l q),(H p,l q),(G p,l q) and (B p,l q) with 0【p≤1 and p≤q≤∞ are ob...This paper describes characteristics of (A p,α,l q) with 0【p≤1,α】0 and p≤q≤∞. As the corollaries, the characteristics of (A p,l q),(H p,l q),(G p,l q) and (B p,l q) with 0【p≤1 and p≤q≤∞ are obtained. (H p,l q) and (H p,H q) with 1【p【∞ and 1≤q≤∞ are also studied.展开更多
Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Freml...Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.展开更多
The criterion for k-smooth points of the Orlicz sequence space endowed with the Orlicz norm is proved. The necessary and sufficient conditions of k-smoothness of l M and l （M ） are obtained, respectively. Finally, w...The criterion for k-smooth points of the Orlicz sequence space endowed with the Orlicz norm is proved. The necessary and sufficient conditions of k-smoothness of l M and l （M ） are obtained, respectively. Finally, we give the counterexamples which show that previous results are not true.展开更多
In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1....In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G （u, v; △） on the sequence space gl.展开更多
By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg n...By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak_Orlicz sequence space with Orlicz norm are given.展开更多
The idea of difference sequence sets X（△） = {x = （xk） ： △x ∈ X} with X = l∞, c and co was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence sp...The idea of difference sequence sets X（△） = {x = （xk） ： △x ∈ X} with X = l∞, c and co was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence spaces and give some inclusion relations.展开更多
In this paper, we introduce the sequence space e^r（u,p） and investigate its some topological and geometrical properties such as basis, α-,β-, γ- duals and the uniform Opial property.
The sufficient and necessary conditions of the Bochner-Orlicz sequence spaces equipped with the Luxemburg norm, which have λ property, are given. The result shows, which is not as usual, that the λ property of the B...The sufficient and necessary conditions of the Bochner-Orlicz sequence spaces equipped with the Luxemburg norm, which have λ property, are given. The result shows, which is not as usual, that the λ property of the Bochner-Orlicz sequence spaces can not be lift from X.展开更多
In this paper we define a sequence space using Orlicz functions. We give certain properties and inclusion relations between known sequence spaces and new sequence space.
In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function.Finall...In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function.Finally,as an immediate consequence of the criteria considered in this paper,the criteria of the weakly compact sets of Orlicz sequence spaces are deduced.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
Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Alta...Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.展开更多
In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞ using m^(th)- difference.We study their properties like completeness,solidness,symm...In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞ using m^(th)- difference.We study their properties like completeness,solidness,symmetricity.Also we obtain some inclusion relations involving the spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and[N_θ,M,Δ~m]_∞ and the Cesàro summable and strongly Cesàro summable sequences.展开更多
文摘In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-difference means are in the linear space l（p） defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l（u, v, p, △（m）） to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp（U, v, △（m）） （1 ≤ p 〈 ∞）.
文摘In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _duals. The criterions of bounded sets in l 1(X) and l ∞(X ) with respect to the weak topologies generated by the σ _duals are obtained. Furthermore, a Schur type result and an automatic continuity theorem of matrix transformation are established.
文摘In this paper, we discuss some basic properties of the Orlicz-Bochner sequence space l_M(X) and its subspace h_M(X). We present the equivalent definition of h_M(X), the sufficient and necessary conditions under which l_^(M) (X) is complete, and l_M(X) and h_M(X) are separable respectively, and also give the sufficient condition that h_M(X) has a basis. All these results generalize the results for the classical Orlicz sequence spaces.
文摘In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr） is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N.
基金supported by the National Science Foundation of China(11271248 and 11302002)the National Science Research Project of Anhui Educational Department(KJ2012Z127)the PhD research startup foundation of Anhui Normal University
文摘In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.
文摘In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces？∞, c and c0 according to a new matrix operator W which is obtained by matrix product.
文摘This paper describes characteristics of (A p,α,l q) with 0【p≤1,α】0 and p≤q≤∞. As the corollaries, the characteristics of (A p,l q),(H p,l q),(G p,l q) and (B p,l q) with 0【p≤1 and p≤q≤∞ are obtained. (H p,l q) and (H p,H q) with 1【p【∞ and 1≤q≤∞ are also studied.
文摘Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.
基金Project supported by the National Natural Science Foundation of China (Grant No.10971129)
文摘The criterion for k-smooth points of the Orlicz sequence space endowed with the Orlicz norm is proved. The necessary and sufficient conditions of k-smoothness of l M and l （M ） are obtained, respectively. Finally, we give the counterexamples which show that previous results are not true.
基金Sponsored by the National NSFC under grant No.19771063
文摘In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
文摘In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G （u, v; △） on the sequence space gl.
文摘By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak_Orlicz sequence space with Orlicz norm are given.
文摘The idea of difference sequence sets X（△） = {x = （xk） ： △x ∈ X} with X = l∞, c and co was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence spaces and give some inclusion relations.
文摘In this paper, we introduce the sequence space e^r（u,p） and investigate its some topological and geometrical properties such as basis, α-,β-, γ- duals and the uniform Opial property.
基金Project supported by the National Natural Science Foundation of China (Grant No.10671118)
文摘The sufficient and necessary conditions of the Bochner-Orlicz sequence spaces equipped with the Luxemburg norm, which have λ property, are given. The result shows, which is not as usual, that the λ property of the Bochner-Orlicz sequence spaces can not be lift from X.
文摘In this paper we define a sequence space using Orlicz functions. We give certain properties and inclusion relations between known sequence spaces and new sequence space.
基金Supported by the National Natural Science Foundation of China(Grant No.11771273)。
文摘In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function.Finally,as an immediate consequence of the criteria considered in this paper,the criteria of the weakly compact sets of Orlicz sequence spaces are deduced.
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〈∞.
文摘Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.
文摘In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞ using m^(th)- difference.We study their properties like completeness,solidness,symmetricity.Also we obtain some inclusion relations involving the spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and[N_θ,M,Δ~m]_∞ and the Cesàro summable and strongly Cesàro summable sequences.
