Almost convergence and generalized difference matrix

Abstract

Let f denotes the space of almost convergent sequences introduced by Lorentz [G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190] and (f) over cap also be the domain of the generalized difference matrix B(r, s) in the sequence space f. In this paper, the beta- and gamma-duals of the spaces f, fs and (f) over cap are determined. Furthermore, two basic results on the space f are proved and the classes ((f) over cap: mu) and (mu: (f) over cap) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where mu is any given sequence space. (C) 2010 Elsevier Ltd. All rights reserved.