ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX

doi:10.1016/S0252-9602(14)60010-2

摘要/Abstract

摘要：

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 f₀(B) and f(B) be the domain of the double sequentialband matrix B(r, s) in the sequence spaces f₀ and f. In this article, the β− and −duals of the space f(B) are determined. Additionally, we give some inclusion theorems concerning with the spaces f₀(B) and f(B). 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.

关键词: Almost convergence, matrix domain of a sequence space, generalized difference matrix, β&minus, and γ−duals and matrix transformations

Abstract:

Key words: Almost convergence, matrix domain of a sequence space, generalized difference matrix, β&minus, and γ−duals and matrix transformations

中图分类号:

46A45

Murat CANDAN. ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX[J]. 数学物理学报(英文版), 2014, 34(2): 354-366.

Murat CANDAN. ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX[J]. Acta mathematica scientia,Series B, 2014, 34(2): 354-366.

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