THE SPACES OF CESÀRO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMS

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

Abstract

Abstract:

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.

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

CLC Number:

46A45

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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