Characterization of Absolute Summability Factors

Abstract

By ( A, B) we denote the set of all sequences λ = (λ n) such that Σ a n λ n is summable B, whenever Σ a n is summable A, where A and B are summability methods. In the present paper we characterize the sets (| N̄, p n |, | N̄, q n | k ) and (| N̄, p n | k , | N̄, q n |), 1 ≤ k < ∞, using functional analytic techniques, and also extend some known results.