Almost convergence and triple band matrix


Sonmez A.

MATHEMATICAL AND COMPUTER MODELLING, vol.57, pp.2393-2402, 2013 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 57
  • Publication Date: 2013
  • Doi Number: 10.1016/j.mcm.2011.11.079
  • Title of Journal : MATHEMATICAL AND COMPUTER MODELLING
  • Page Numbers: pp.2393-2402

Abstract

The concept of almost convergence of a bounded sequence x = (x(k)) was introduced by means of Banach Limits by G.G. Lorentz [G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948) 167-190]. The space of almost convergent sequences is denoted by f. In this paper, we introduce f (B), which is the domain of triple band matrix B(r, s, t) in the sequence space f, determine the beta- and gamma-duals of the spaces f (B) and characterize the classes (f (B) : Y) and (Y : f (B)), where Y is any given sequence space. Finally, we also give the characterizations of some other classes as an application of those main results. Published by Elsevier Ltd