Almost convergence and generalized difference matrix

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