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Domain of the double sequential band matrix B() on some maddox's spaces

Authors
  • ÖZGER, Faruk
  • BAŞAR, Feyzi1
  • 1 Department of Mathematics
Type
Published Article
Journal
Acta Mathematica Scientia
Publication Date
Jan 01, 2014
Volume
34
Issue
2
Pages
394–408
Identifiers
DOI: 10.1016/S0252-9602(14)60014-X
Source
Elsevier
Keywords
License
Unknown

Abstract

The domain of generalized difference matrix B(r, s) in the classical spaces ℓ∞, c, and c0 was recently studied by Kirişçi and Başar in [16]. The main goal of this article is to introduce the paranormed sequence spaces ℓ∞(), c(), and c0(), 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∞(), c(), and c0() are computed and the bases of the spaces c() and c0() are constructed. The final section of this article is devoted to the characterization of the classes (λ() : μ) and (μ : λ()), 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.

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