Matrix Transformations Between Some Vector-Valued Sequence Spaces

Abstract

In this paper, we give necessary and sufficient conditions for infinite matrices mapping from the Nakano vector-valued sequence space l(X, p) into any BK-space, and by using this result, we obtain the matrix characterizations from l(X, p) into the sequence spaces l∞(Y), c0(Y, q), c(Y), l s (Y), E r (Y), and F r (Y), where p = (p k ) and q = (q k ) are bounded sequences of positive real numbers such that p k ≤ 1 for all k ∈ N, r ≥ 0, and s ≥ 1.