数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (2): 394-408.doi: 10.1016/S0252-9602(14)60014-X

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

 Faruk ÖZGER, Feyzi BASAR   

  1. Department of Mathematics, Fatih University, HadimkÖy Campus, 34500, Buyuk¸cekmece, Istanbul, Turkey
  • 收稿日期:2012-08-13 修回日期:2013-04-20 出版日期:2014-03-20 发布日期:2014-03-20
  • 基金资助:

    The main results of this article was partially presented at First International Conference on Analysis and Applied Mathematics (ICAAM 2012) held October 18-21, 2012 in Gumushane, Turkey at Gumushane University.

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

 Faruk ÖZGER, Feyzi BASAR   

  1. Department of Mathematics, Fatih University, HadimkÖy Campus, 34500, Buyuk¸cekmece, Istanbul, Turkey
  • Received:2012-08-13 Revised:2013-04-20 Online:2014-03-20 Published:2014-03-20
  • Supported by:

    The main results of this article was partially presented at First International Conference on Analysis and Applied Mathematics (ICAAM 2012) held October 18-21, 2012 in Gumushane, Turkey at Gumushane University.

摘要:

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), cB, 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.

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

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), cB, 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

中图分类号: 

  • 46A45