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
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
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
Two kinds of convergent sequences on the real vector space m of all bounded sequences in a real normed space X were discussed in this paper, and we prove that they are equivalent, which improved the results of [1].
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.
基金Foundation item： the National Natural Science Foundation of China （No. 10871101） the Research Fund for the Doctoral Program of Higher Education （No. 20060055010）Acknowledgments The author would like to thank Professor Ding Guanggui for his encouragement and advice.
文摘Two kinds of convergent sequences on the real vector space m of all bounded sequences in a real normed space X were discussed in this paper, and we prove that they are equivalent, which improved the results of [1].
