On compact operators and some Euler B(m)-difference sequence spaces

KARA E. E., Başarir M.

Journal of Mathematical Analysis and Applications, vol.379, no.2, pp.499-511, 2011 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 379 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.1016/j.jmaa.2011.01.028
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.499-511
  • Keywords: α-, B(m)-difference sequence spaces, Compact operators, Hausdorff measure of noncompactness, Matrix transformations, Schauder basis
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

Altay and Başar (2005) [1] and Altay, Başar and Mursaleen (2006) [2] introduced the Euler sequence spaces e0t, ect and e∞t. Başarir and Kayikçi (2009) [3] defined the B(m)-difference matrix and studied some topological and geometric properties of some generalized Riesz B(m)-difference sequence space. In this paper, we introduce the Euler B(m)-difference sequence spaces e0t(B(m)), ect(B(m)) and e∞t(B(m)) consisting of all sequences whose B(m)-transforms are in the Euler spaces e0t, ect and e∞t, respectively. Moreover, we determine the α-, β- and γ-duals of these spaces and construct the Schauder basis of the spaces e0t(B(m)) and ect(B(m)). Finally, we characterize some matrix classes concerning the spaces e0t(B(m)) and ect(B(m)) and give the characterization of some classes of compact operators on the sequence spaces e0t(B(m)) and e∞t(B(m)). © 2011 Elsevier Inc.