On matrix mappings into some strong Cesàro sequence spaces

摘要

We determine the classes (X, YT) of matrix transformations from X into YT where X is one of the classical sequence spaces c0, c, ℓ∞ and ℓ1 of all null, convergent and bounded complex sequences and all absolutely convergent complex series, T is a triangle, YT is the matrix domain of T in Y and Y is any of the sets of all sequences that are summable, summable to zero or bounded by the strong Cesàro method of order 1, with index 1 ⩽ p < ∞. Furthermore, we determine the representations of the general bounded linear operators from c into Y. We also establish estimates for the norms of the operators in each case.