Almost convergence and generalized difference matrix

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 also be the domain of the generalized difference matrix B(r, s) in the sequence space f . In this paper, the β- and γ -duals of the spaces f , fs andf are determined. Furthermore, two basic results on the space f are proved and the classes (f : μ) and (μ:f ) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is any given sequence space.