Banach algebras of matrix transformations between some sequence spaces related to Λ-strong convergence and boundedness

We study the spaces c0(Λ),c(Λ)c0(Λ),c(Λ) and c∞(Λ)c∞(Λ) of sequences that are Λ-strongly convergent to zero, Λ-strongly convergent and Λ-strongly bounded, and the related spaces v0(Λ)v0(Λ) and v∞(Λ)v∞(Λ). In particular, we give the characterizations of several classes of matrix transformations between those spaces. Furthermore, we use our results to prove that the classes of matrix transformations from v∞(Λ),c∞(Λ)v∞(Λ),c∞(Λ) and c(Λ)c(Λ) into themselves are Banach algebras. As an application of our results, we establish an estimate for the Hausdorff measure of noncompactness of matrix operators that map c(Λ)c(Λ) into itself, give a characterization of the subclass of compact operators, and a sufficient condition for those operators to be Fredholm.