Spaces of AλAλ-almost null and AλAλ-almost convergent sequences

In the present paper, by defining the notion of AλAλ-almost nullity and AλAλ-almost convergence of sequences we introduce the spaces Aλ(f0)Aλ(f0) and Aλ(f)Aλ(f) of AλAλ-almost null and AλAλ-almost convergent sequences. Moreover, we establish some inclusion relations concerning with those spaces and determine the alpha-, beta- and gamma-duals of the space Aλ(f)Aλ(f). Finally, two basic results on the characterization of the classes (Aλ(f):μ)(Aλ(f):μ) and (μ:Aλ(f))(μ:Aλ(f)) of infinite matrices are given, and the characterizations of some other classes are also derived as an application of those main results, where μμ is any given sequence space.