On the B-difference sequence space derived by generalized weighted mean and compact operators

Başarir M., KARA E. E.

Journal of Mathematical Analysis and Applications, vol.391, no.1, pp.67-81, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 391 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.1016/j.jmaa.2012.02.031
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.67-81
  • Keywords: α-, β-, γ-duals, B-difference sequence spaces, Compact operators, Hausdorff measure of noncompactness, Matrix mappings, Paranormed sequence spaces, Weighted mean
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In the present paper, by using generalized weighted mean and difference matrix B, we introduce the paranormed sequence space ℓ(u,v,p;B) which consist of all sequences whose generalized weighted B-difference means are in the linear space ℓ(p) introduced by I.J. Maddox. Also, we give the basis of this space and compute its α-, β- and γ-duals. Further, we characterize the classes of matrix mappings from ℓ(u,v,p;B) to ℓ ∞, c and c 0. Finally, we apply the Hausdorff measure of noncompactness to characterize some classes of compact operators given by matrices on the space ℓp(u,v;B) (1≤p<∞). © 2012 Elsevier Inc.