On some difference sequence spaces of weighted means and compact operators

BaŞarir M., KARA E. E.

Annals of Functional Analysis, vol.2, no.2, pp.114-129, 2011 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 2 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.15352/afa/1399900200
  • Journal Name: Annals of Functional Analysis
  • Journal Indexes: Scopus
  • Page Numbers: pp.114-129
  • Keywords: Bk spaces, Compact operators, Hausdorff measure of noncompactness, Matrix mappings, Weighted mean
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In the peresent paper, by using generalized weighted mean and difference matrix of order m, we introduce the sequence spaces X(u, v, Δ(m)), where X is one of the spaces ℓ∞, c or c0. Also, we determine the α-, β-and γ-duals of those spaces and construct their Schauder bases for X ∈ (c, c0). Morever, we give the characterization of the matrix mappings on the spaces X(u, v, Δm) for X ∈ (ℓ∞, c, c0). Finally, we characterize some classes of compact operators on the spaces ℓ∞(u, v, Δm) and c0(u, v, Δm) by using the Hausdorff measure of noncompactness. © 2011, Duke University Press. All rights reserved.