In this study, as the domain of four dimensional Euler mean E(r,s) of orders r,sin the space L_p for 0 < p < 1, we examine the double sequence space ε_p^(r,s) and some properties of four dimensional Euler mean....In this study, as the domain of four dimensional Euler mean E(r,s) of orders r,sin the space L_p for 0 < p < 1, we examine the double sequence space ε_p^(r,s) and some properties of four dimensional Euler mean. We determine the α-and β(bp)-duals of the space εp r,s, and characterize the classes(ε_p^(r,s):M_u),(ε_p^(r,s):C_(bp)) and(ε_p^(r,s):L_q) of four dimensional matrix transformations, where 1 ≤q < ∞. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.展开更多
The domain of generalized difference matrix B（r, s） in the classical spaces L∞, e, and co was recently studied by Kirisci and Basar in [16]. The main goal of this article is to introduce the paranormed sequence spa...The domain of generalized difference matrix B（r, s） in the classical spaces L∞, e, and co was recently studied by Kirisci and Basar in [16]. The main goal of this article is to introduce the paranormed sequence spaces L∞（B,p）, c（B,p）, and co（B,p）, which are more general and comprehensive than the corresponding consequences of the matrix domain of B（r, s）, as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces L∞ （B, p）, c（B, p）, and co （B, p） are computed and the bases of the spaces c（B, p） and co （B, p） are constructed. The final section of this article is devoted to the characterization of the classes （λ（B, p）： μ） and （μ：λ（B, p））, where λ ∈ {c, co, L∞ } and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of Mmost convergent sequences is obtained by means of a given lemma.展开更多
As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the ...As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.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 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
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 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
Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the ...Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the l_(p)-norm of the matrix A^(ru)and as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain l_(p)(A^(ru)).展开更多
In this note, we establish several results concerning the gliding hump properties of matrix domains. In order to discuss F-WGHP, we introduce the UAK-property and find that this sort of property has close relationship...In this note, we establish several results concerning the gliding hump properties of matrix domains. In order to discuss F-WGHP, we introduce the UAK-property and find that this sort of property has close relationship with F-WGHP. In the course of discussing F-WGHP and WGHP of （C0）cn, we discuss the F-WGHP and WGHP of the almost-null sequence space f0.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.
Let λ and μ be sequence spaces and have both the signed weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ . In this paper, it is proved ...Let λ and μ be sequence spaces and have both the signed weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ . In this paper, it is proved that if λ and μ are β spaces and λ β and μ β have also the signed weak gliding hump property, then for any polar topology τ, ((λ,μ),τ) is always sequentially complete locally convex topological algebra.展开更多
The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（...The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（B） be the domain of the double sequential band matrix B（r, s） in the sequence spaces f0 and f. In this article, the β- and γ-duals of the space f（B） are determined. Additionally, we give some inclusion theorems concerning with the spaces f0（B） and f（β）. Moreover, the classes （f（B） ： μ） and （μ： f（B）） of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space.展开更多
In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.
Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order dif...Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order differences of x and Δu^（m）X = {x=（x）k=0^∞ uΔ（m）x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^（m）X for X=co（p）,c（p）,l∞（p） and characterize some matrix transformations between these spaces Δ^（m）X.展开更多
SINCE Michael (1952) published the first book about topological algebras, it has become abranch of functional analysis. Applications of topological algebras have been found in complexanalysis of several variables, dif...SINCE Michael (1952) published the first book about topological algebras, it has become abranch of functional analysis. Applications of topological algebras have been found in complexanalysis of several variables, differential geometry, unbounded operator and others, and alge-braic topology, k-theory and others have been applied to topological algebras (see, for exam-ple, ref.[2]). It is well known that the set of all continuous linear operators on Banach spaceconstitutes a Banach algebra, so it is obviously meaningful to study the topological algebra con-stituted by the set of all continuous linear operators on concrete topological vector space. It展开更多
文摘In this study, as the domain of four dimensional Euler mean E(r,s) of orders r,sin the space L_p for 0 < p < 1, we examine the double sequence space ε_p^(r,s) and some properties of four dimensional Euler mean. We determine the α-and β(bp)-duals of the space εp r,s, and characterize the classes(ε_p^(r,s):M_u),(ε_p^(r,s):C_(bp)) and(ε_p^(r,s):L_q) of four dimensional matrix transformations, where 1 ≤q < ∞. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.
文摘The domain of generalized difference matrix B（r, s） in the classical spaces L∞, e, and co was recently studied by Kirisci and Basar in [16]. The main goal of this article is to introduce the paranormed sequence spaces L∞（B,p）, c（B,p）, and co（B,p）, which are more general and comprehensive than the corresponding consequences of the matrix domain of B（r, s）, as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces L∞ （B, p）, c（B, p）, and co （B, p） are computed and the bases of the spaces c（B, p） and co （B, p） are constructed. The final section of this article is devoted to the characterization of the classes （λ（B, p）： μ） and （μ：λ（B, p））, where λ ∈ {c, co, L∞ } and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of Mmost convergent sequences is obtained by means of a given lemma.
文摘As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.
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））.
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 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Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the l_(p)-norm of the matrix A^(ru)and as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain l_(p)(A^(ru)).
文摘In this note, we establish several results concerning the gliding hump properties of matrix domains. In order to discuss F-WGHP, we introduce the UAK-property and find that this sort of property has close relationship with F-WGHP. In the course of discussing F-WGHP and WGHP of （C0）cn, we discuss the F-WGHP and WGHP of the almost-null sequence space f0.
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Supported by Natural Science Foundations of China (11101108, 11171301, 10771191 and 10471124)Natural Science Foundation of Zhejiang Province of China (Y6090105)
文摘Let X and Y be Banach spaces, 0 〈 q 〈 ＋∞, i ≤ p 〈 ＋∞. In this paper, we characterize matrix transformations of lq （ X ） to lp （ Y ）.
基金This research is partly supported by the NSF of Hei Longjiang
文摘Let λ and μ be sequence spaces and have both the signed weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ . In this paper, it is proved that if λ and μ are β spaces and λ β and μ β have also the signed weak gliding hump property, then for any polar topology τ, ((λ,μ),τ) is always sequentially complete locally convex topological algebra.
文摘The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（B） be the domain of the double sequential band matrix B（r, s） in the sequence spaces f0 and f. In this article, the β- and γ-duals of the space f（B） are determined. Additionally, we give some inclusion theorems concerning with the spaces f0（B） and f（β）. Moreover, the classes （f（B） ： μ） and （μ： f（B）） of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space.
文摘In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.
基金the German DAAD Foundation(German Academic Exchange Service)Grant No.911 103 012 8the Research Project #1232 of the Serbian Ministry of Science,Technology and Development
文摘Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order differences of x and Δu^（m）X = {x=（x）k=0^∞ uΔ（m）x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^（m）X for X=co（p）,c（p）,l∞（p） and characterize some matrix transformations between these spaces Δ^（m）X.
文摘SINCE Michael (1952) published the first book about topological algebras, it has become abranch of functional analysis. Applications of topological algebras have been found in complexanalysis of several variables, differential geometry, unbounded operator and others, and alge-braic topology, k-theory and others have been applied to topological algebras (see, for exam-ple, ref.[2]). It is well known that the set of all continuous linear operators on Banach spaceconstitutes a Banach algebra, so it is obviously meaningful to study the topological algebra con-stituted by the set of all continuous linear operators on concrete topological vector space. It
