DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r, s) ON SOME MADDOX´S SPACES

doi:10.1016/S0252-9602(14)60014-X

Abstract

Abstract:

The domain of generalized difference matrix B(r, s) in the classical spaces l_∞, c, and c₀ was recently studied by Kiri¸s¸ci and Ba¸sar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l_∞(B, p), c( B, p), and c₀(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 c₀(eB , p) are computed and the bases of the spaces c(B , p) and c₀(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, c₀, l_∞} and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma.

Key words: Matrix domain, double sequential band matrices, almost convergence, para-normed spaces, matrix transformations

CLC Number:

46A45

Faruk OZGER, Feyzi BASAR. DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r, s) ON SOME MADDOX´S SPACES[J].Acta mathematica scientia,Series B, 2014, 34(2): 394-408.

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