THE SPACES OF CESÀRO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMS

doi:10.1016/S0252-9602(12)60176-3

摘要/Abstract

摘要：

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 e f and e f₀ consisting of all sequences whose Cesàro transforms of order one are in the spaces f and f₀, respectively. Also, in this paper, we show that e f and e f₀ are linearly isomorphic to the spaces f and f₀, respectively. The β- and γ-duals of the spaces e f and e f₀ 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) Bc-core(x), Bc-core(Ax) Bc-core(x), Bc-core(Ax) st-core(x) for all x ∈l₁.

关键词: almost convergence, matrix domain of a sequence space, β- and γ-duals and matrix transformations, core theorems, isomorphism

Abstract:

Key words: almost convergence, matrix domain of a sequence space, β- and γ-duals and matrix transformations, core theorems, isomorphism

中图分类号:

46A45

Kuddusi Kayaduman, Mehmet S?eng¨on¨ul. THE SPACES OF CESÀRO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMS[J]. 数学物理学报(英文版), 2012, 32(6): 2265-2278.

Kuddusi Kayaduman, Mehmet S?eng¨on¨ul. THE SPACES OF CESÀRO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMS[J]. Acta mathematica scientia,Series B, 2012, 32(6): 2265-2278.

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