The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80(1948), 167–190]. Let f0() and f() be the domain of the double sequential band matrix () in the sequence spaces f0 and f. In this article, the β. and γ-duals of the space f() are determined. Additionally, we give some inclusion theorems concerning with the spaces f0() and f(). Moreover, 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 an arbitrary sequence space.