A Characterization of Absolute Summability Factors

Abstract

Let A and B be two summability methods. We shall use the notation lambda is an element of (A, B) to denote the set of all sequences lambda such that Sigmaa(n)lambda(n) is summable B, whenever Sigmaa(n) is summable A. In the present paper we characterize the sets lambda is an element of (\N,p(n)\, \T\(k)) and lambda is an element of (\(N) over bar ,p(n)\, \T\), where T is a lower triangular matrix with positive entries and row sums 1. As special cases we obtain summability factor theorems and inclusion theorems for pairs of weighted mean matrices.